# MCQs: Ch 04 Quadratic Equations

High quality MCQs of Chapter 01 Number System of Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore. The answers are given at the end of the page.

### MCQs

- An equation $ax^2+bx+c=0$ is called
- Linear
- Quadratic
- Cubic equation
- None of these

- For a quadratic equation $ax^2+bx+c=0$
- $b \neq 0$
- $c \neq 0$
- $a \neq 0$
- None of these

- Another name for a quadratic equation in $x$ is
- 2nd degree
- Linear
- Cubic
- None of these

- Number of basic techniques for solving a quadratic equation are
- Two
- Three
- Four
- None of these

- The solutions of the quadratic equation are also called its
- Factors
- Roots
- Coefficients
- None of these

- Maximum number of roots of a quadratic equation are
- One
- Two
- Three
- None of these

- An expression of the form $ax^2+bx+c$ is called
- Polynomial
- Equation
- Identity
- None of these

- If $ax^2+bx+c=0$, then $\{a,b\}$ is called
- Factors
- Solution set
- Roots
- None of these

- Equation having same solution are called
- Exponential equations
- Radical equations
- Simultaneous equations
- Reciprocal equations

- The Quadratic formula for $ax^2+bx+c=0$, $a\neq 0$ is
- $x= \frac{b \pm \sqrt{b^2-4ac}}{a}$
- $x= \frac{-b \pm \sqrt{b^2+4ac}}{2a}$
- $x= \frac{-b \pm \sqrt{4ac-b^2}}{2a}$
- $x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

- A quadratic equation which cannot be solved by factorization, that will be solved by
- Comparing coefficients
- Completing square
- Both $A$ and $B$
- None of these

- If we solve $ax^2+bx+c=0$ by complete square method, we get
- Cramer's rule
- De Morgan's Law
- Quadratic formula
- None of these

- Equations, in which the variable occurs in exponent, are called
- Reciprocal Equations
- Exponential Equations
- Radical Equations
- None of these

- Equations, which remains unchanged when $x$ is replaced by $\frac{1}{x}$ are called
- Reciprocal Equations
- Radical Equations
- Exponential Equations
- None of these

- Each complex cube root of unity is
- Cube of the other
- Square of the other
- Bi-square of the other
- None of these

- The sum of all the three cube roots of unity is
- Unity
- -ve
- +ve
- Zero

- The product of all the three cube roots of unity is
- Zero
- -ve
- Unity
- Two

- For any $n \in Z$, $w^n$ is equivalent to one of the cube roots of
- Unity
- $8$
- $27$
- $64$

- The sum of the four fourth roots of unity is
- Unity
- -ve
- +ve
- Zero

- The product of all the four fourth roots of unity is
- $1$
- $-1$
- $2$
- $-2$

- Both the complex fourth roots of unity are
- Reciprocal of each other
- Conjugate of each other
- Additive inverse
- Multiplicative inverse

- Both the real fourth roots of unity are
- Reciprocal of each other
- Conjugate of each other
- Additive inverse
- Multiplicative inverse

- An expression of the form $a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$ is called
- Quadratic equation
- Polynomial in $x$
- Non-linear equation
- None of these

- A polynomial in$x$ can be considered as a
- Non-linear equation
- Polynomial function of $x$
- Both $A$ and $B$
- None of these

- The highest power of $x$ in polynomial in $x$ is called
- Coefficient of polynomial
- Exponent of polynomial
- Degree of polynomial
- None of these

- $(\frac{-1-\sqrt{3i}}{2})^5$ is equal to
- $\frac{1-\sqrt{3i}}{2}$
- $\frac{-1-\sqrt{3i}}{2}$
- $\frac{-1+\sqrt{3}}{2}$
- $\frac{-1+\sqrt{3i}}{2}$

- If $w$ is the complex root of unity then its conjugate is
- $-w$
- $-w^2$
- $w^2$
- $w^3$

- If a polynomial $f(x)$ of degree $x \geq 1$ is divided by $(x-a)$ then reminder is
- $a$
- $f(a)$
- $n$
- None of these

- If a polynomial $f(x)=x^3+4x^2-2x+5$ is divided by $(x-1)$ then the reminder is
- $4$
- $2$
- $8$
- $0$

- If $(x-a)$ is the factor of a polynomial $f(x)$ then $f(a)=$
- $1$
- $0$
- $2$
- $-1$

- There is a nice short cut method for long division of polynomial $f(x)$ by $(x-a)$ is called
- Factorization
- Rationalization
- Synthetic division
- None of these

- If a polynomial $f(x)$ is divided by $(x+a)$ then the reminder is
- $f(a)$
- $f(-a)$
- $0$
- None of these

- If $x^3+3x^2-6x+2$ is divided by $x+2$ then the reminder
- $-18$
- $9$
- $-9$
- $18$

- The graph of a quadratic function
- Hyperbola
- Straight line
- Parabola
- Triangle

- If $x-1$ is a factor of $5x^2+10x-a$ then $a=$
- $n(B)$
- $n(A)$
- $\phi$
- non-empty

- The sum of the roots of the equation $ax^2+bx+c=0$ is
- $\displaystyle\frac{b}{a}$
- $\displaystyle\frac{b}{c}$
- $\displaystyle\frac{c}{a}$
- $-\displaystyle\frac{b}{a}$

- The sum of the roots of the equation $ax^2-bx+c=0$ is
- $\displaystyle\frac{b}{c}$
- $\displaystyle\frac{b}{a}$
- $-\displaystyle\frac{b}{a}$
- $-\displaystyle\frac{c}{a}$

- The product of the roots of the equation $ax^2+bx+c=0$ is
- $\displaystyle\frac{b}{c}$
- $\displaystyle\frac{b}{a}$
- $\displaystyle\frac{c}{a}$
- $-\displaystyle\frac{c}{a}$

- The product of the roots of the equation $ax^2-bx+c=0$ is
- $\displaystyle\frac{c}{a}$
- $\displaystyle\frac{b}{a}$
- $\displaystyle\frac{a}{b}$
- $-\displaystyle\frac{c}{a}$

- If $S$ and $P$ are sum and product of the roots of a quadratic equation then
- $x^2+Sx+p=0$
- $x^2+Sx-p=0$
- $x^2-Sx-p=0$
- $x^2-Sx+p=0$

- For what value of $K$ will equation $x^2-Kx+4=0$ have sum of roots equal to product of roots
- $3$
- $-2$
- $-4$
- $4$

- The nature of the roots of quadratic equation depends upon the value of the expression
- $b^2+4ac$
- $4ac-b^2$
- $b^2-4ac$
- None of these

- If $ax^2+bx+c=0$, $a\neq 0$ then expression $(b^2-4ac)$ is called
- Quotient
- Reminder
- Discriminant
- None of these

- If roots of $ax^2+bx+c=0$ are equal then $b^2-4ac$ is equal to
- $1$
- $-1$
- $0$
- None of these

- If roots of $ax^2+bx+c=0$ are imaginary then
- $b^2-4ac=0$
- $b^2-4ac<0$
- $b^2-4ac>0$
- None of these

- If roots of $ax^2+bx+c=0$ are rational then $b^2-4ac$ is
- $-ve$
- Perfect square
- Not a perfect square
- None of these

- If roots of $ax^2+bx+c=0$ are real and unequal then $b^2-4ac$ is
- $-ve$
- Zero
- $+ve$
- None of these

- If $xy$ term is missing coefficients of $x^2$ and $y^2$ are equal in two $2$nd degree equations then by subtraction, we get
- Non-linear equation
- Linear equation
- Quadratic equation
- None of these

- If one root of quadratic equation is $a- \sqrt{b}$ then the other root is
- $\sqrt{a}-b$
- $\sqrt{a}+b$
- $-a+\sqrt{b}$
- $a+\sqrt{b}$

- If $\alpha$, $\beta$ are the roots of a quadratic equation then
- $(\alpha x)(\beta x)=0$
- $(\alpha +x)(\alpha +\beta)=0$
- $(x-\alpha)(x- \beta)=0$
- $(x+\alpha)(x+\beta)=0$

- $4x^2-9=0$ is called
- Quadratic equation
- Purely quadratic
- Linear equation
- Quadratic polynomial

- Roots of $x^2-4=0$ are
- $2,2$
- $\pm 2i$
- $-2,2$
- $-2,-2$

- $w^{15}= ----- $
- $1$
- $-1$
- $i$
- $-i$

- Equation whose roots are $2$, $3$ is
- $x^2+5x+6=0$
- $x^2-5x+6=0$
- $x^2+x-6=0$
- $x^2-x+6=0$

- Roots of $x^2+4=0$ are
- Real
- Rational
- Irrational
- Imaginary

- Extraneous roots occur in
- Exponential equation
- Reciprocal equation
- Radical equation
- In every equation

- Roots of $x^3=8$ are
- One real
- All imaginary
- One real two imaginary
- Two real one imaginary

- If $1,w,w^2$ are cube roots of unity then $w^n$ ($n$ is positive integer)
- Also must be a root
- May be a root
- is not a root
- $w^n=\pm 1$

- Roots of $x^2-4x+4=0$ are
- Equal
- Unequal
- Imaginary
- Irrational

- Discriminant of $x^2-6x+5=0$ is
- Not a perfect square
- Perfect square
- Zero
- Negative

- Discriminant of $x^2+x+1=0$ is
- $3$
- $-3$
- $3i$
- $-3i$

- Roots of $x^2-5x+6=0$ are
- Real distinct
- Real equal
- Real unequal
- Equal

- $4x^2+ \frac{2}{x}+3$ is a ——
- Polynomial of degree $2$
- Polynomial of degree $1$
- Quadratic equation
- None of these

- The solution set of $x^2-7x+10=0$ is
- $\{7,10\}$
- $\{2,5\}$
- $\{5,10\}$
- None of these

- If a polynomial $R(x)$ is divided by $x-a$, then the reminder is
- $R(x)$
- $R(a)$
- $R(x-a)$
- $R(-a)$

- If $x^3+4x^2-2x+5$ is divided by $x-1$, then the reminder is
- $-8$
- $6$
- $-6$
- $8$

- The sum of roots of the equation $ax^2+bx+c=0$, $a \neq 0$ is ——
- $\displaystyle{\frac{c}{a}}$
- $\displaystyle{\frac{b}{a}}$
- $\displaystyle{-\frac{b}{a}}$
- $\displaystyle{\frac{a}{c}}$

- The $S$ and $P$ are the sum and product of roots of a quadratic equation, then the quadratic equation is
- $x^2+Sx+P=0$
- $x^2-Sx-P=0$
- $x^2-Sx+P=0$
- $x^2+Sx-P=0$

- The roots of the equations $ax^2+bx+c$ one real and equal if
- $b^2-4ac\geq 0$
- $b^2-4ac> 0$
- $b^2-4ac< 0$
- $b^2-4ac= 0$

- The roots of the equations $ax^2+bx+c=0$ are complex or imaginary if
- $b^2-4ac\geq 0$
- $b^2-4ac> 0$
- $b^2-4ac< 0$
- $b^2-4ac= 0$

- The roots of the equations $ax^2+bx+c$ are real and distinct if
- $b^2-4ac\geq 0$
- $b^2-4ac> 0$
- $b^2-4ac< 0$
- $b^2-4ac= 0$

- If the roots of $2x^2+kx+8=0$ are equal then $k=-----$
- $\pm 16$
- $64$
- $32$
- $\pm8$

- If $w$ is a cube root of unity, then $1+w+w^2=----$
- $-1$
- $0$
- $1$
- $2$

- The roots of a equation will be equal if $b^2-4ac$ is
- $<0$
- $>0$
- $0$
- $1$

- The roots of a equation will be irrational if $b^2-4ac$ is
- Positive and perfect square
- Positive but not perfect square
- Negative and perfect square
- Negative but not a perfect square

- The product of cube roots of unity is
- $0$
- $-1$
- $1$
- None of these

- For any integer $k$, $w^n=$ when $n=3k$
- $0$
- $1$
- $w$
- $w^2$

- $w^{29}=$
- $0$
- $1$
- $w$
- $w^2$

- $(3+w)(2+w^2)=$
- $1$
- $2$
- $3$
- $4$

- $w^{28}+w^{29}=$
- $1$
- $-1$
- $w$
- $w^2$

- There are —– basic techniques for solving a quadratic equation
- Two
- Three
- Four
- None of these

- If $w=\displaystyle{\frac{-1+\sqrt{3}i}{2}}$ then $w^2=$
- $\displaystyle{\frac{-1+\sqrt{3}i}{2}}$
- $\displaystyle{\frac{1+\sqrt{3}i}{2}}$
- $\displaystyle{\frac{-1-\sqrt{3}i}{2}}$
- None of these

- The sum of the four fourth roots of unity is
- $0$
- $1$
- $2$
- $3$

- The product of the four fourth roots of unity is
- $0$
- $1$
- $-1$
- $i$

- The polynomial $x-a$ is a factor of the polynomial $f(x)$ iff
- $f(a)=0$
- $f(a)$ is negative
- $f(a)$ is positive
- None of these

- Two quadratic equations in which $xy$ term is not present and coefficients of $x^2$ and $y^2$ are equal, give a —— by subtraction.
- Parabola
- Homogeneous equation
- Quadratic equation
- Linear equation

- If $\alpha, \beta$ are roots of $3x^2+2x-5=0$ then $\displaystyle{\frac{1}{\alpha}+\frac{1}{\beta}}=------$
- $\displaystyle{\frac{5}{2}}$
- $\displaystyle{\frac{5}{3}}$
- $\displaystyle{\frac{2}{5}}$
- $\displaystyle{-\frac{2}{5}}$

- The cube roots of $8$ are
- $1,w,w^2$
- $2,2w,2w^2$
- $3,3w,3w^2$
- None of these

- The four fourth roots of unity are
- $0,1,-i,i$
- $0,-1,i,-i$
- $-2,2,2i,-2i$
- None of these

- If $w$ is complex cube root of unity then $w= -----$
- $0$
- $1$
- $w^2$
- $w^{-2}$

- For equal roots of $ax^2+bx+c=0$, $b^2-4ac$ will be
- Negative
- Zero
- $1$
- $2$

- $(1+w-w^2)^8=$
- $4w$
- $16w$
- $64w$
- $256w$

- If $w$ is the imaginary cube root of unity, then the quadratic equation with roots $2w$ and $2w^2$ is
- $x^2+3x+9=0$
- $x^2-3x+9=0$
- $x^2-2x+4=0$
- $x^2+2x+4=0$

- If a polynomial $f(x)$ is divided by a linear divisor $ax+1$, the reminder is
- $\displaystyle{f(\frac{1}{a})}$
- $\displaystyle{-f(\frac{1}{a})}$
- $f(a)$
- $f(-a)$

- If the roots of the quadratic equation $2x^2-4x+5=0$ are $\alpha$ and $\beta$, then $(\alpha+1)(\beta+1)=$
- $\displaystyle{\frac{2}{11}}$
- $\displaystyle{-\frac{2}{11}}$
- $\displaystyle{\frac{11}{2}}$
- None of these

- $x^2+4x+4$ is
- Polynomial
- Equation
- Identity
- None of these

- The graph of quadratic function is
- Circle
- Parabola
- Triangle
- Rectangle

- $w^{65}=$
- $0$
- $1$
- $w$
- $w^2$

- If $\alpha, \beta$ are roots of $3x^2+2x-5=0$, then $\alpha^2+\beta^2=$
- $\displaystyle{\frac{9}{34}}$
- $\displaystyle{-\frac{9}{34}}$
- $\displaystyle{\frac{34}{9}}$
- $\displaystyle{-\frac{34}{9}}$

- If $a>0$, then the function $f(x)=ax^2+bx+c$ has
- Maximum value
- Minimum value
- Constant value
- Positive value

- The product of the roots of equation $5x^2-x+2=0$ is
- $\displaystyle{\frac{5}{2}}$
- $\displaystyle{-\frac{5}{2}}$
- $\displaystyle{\frac{2}{5}}$
- $2$

### Answers

1-b, 2-c, 3-a, 4-b, 5-b, 6-b, 7-a, 8-b, 9-c, 10-d, 11-b, 12-c, 13-b, 14-a, 15-b, 16-d, 17-c, 18-a, 19-d, 20-b, 21-b, 22-c, 23-b, 24-b, 25-c, 26-d, 27-c, 28-b, 29-c, 30-b, 31-c, 32-b, 33-d, 34-c, 35-d, 36-d, 37-b, 38-c, 39-d, 40-d, 41-d, 42-c, 43-c, 44-c, 45-c, 46-b, 47-c, 48-b, 49-d, 50-c, 51-b, 52-c, 53-a, 54-b, 55-d, 56-c, 57-c, 58-d, 59-a, 60-b, 61-b, 62-a, 63-d, 64-b, 65-b, 66-d, 67-c, 68-c, 69-d, 70-c, 71-b, 72-d, 73-b, 74-b, 75-b, 76-c, 77-b, 78-d, 79-d, 80-b, 81-b, 82-c, 83-a, 84-c, 85-a, 86-d, 87-c, 88-b, 89-b, 90-d, 91-b, 92-c, 93-d, 94-b, 95-a, 96-a, 97-b, 98-d, 99-c, 100-a, 101-d