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
$\displaystyle{\frac{5}{2}}$
$\displaystyle{-\frac{5}{2}}$
$\displaystyle{\frac{2}{5}}$
$2$