# Ch 04: Quadratic Equations

- Reduce $x^{-2}-10=3x^{-1}$ to quadratic form —
*BISE Gujrawala(2015)* - Show that $x^3-y^3=(x-y)(x-wy)(x-w^2y)$ —
*BISE Gujrawala(2015)* - If $n$ is an odd integer, is $(x+a)$ factor of $(x^n+a^n)$? —
*BISE Gujrawala(2015)* - If the roots of $px^2+qx+q=0$ are $\alpha$, $\beta$,then prove that $$\sqrt {\frac{\alpha}{\beta}}+\sqrt {\frac{\beta}{\alpha}}+\sqrt{\frac{p}{q}}=0$$ —
*BISE Gujrawala(2017),BISE Sagodha(2017* - Solve the following system of equations —
*BISE Gujrawala(2017)*$${\begin{array}{c} x^2-5xy+6y^2=0\\x^2+y^2=45\end{array}}$$ - Find the roots of the equation $4x^2+7x-1=0$ —
*BISE Gujrawala(2017)* - When the polynomial $x^3+2x^2+kx+4$ is divided by $x-2$, then the reminder is $14$, find $k$. —
*BISE Gujrawala(2017)* - Show that the roots of the equation $x^2-2(m+\frac{1}{m})x+3=0$, $m \neq 0$ will be real —
*BISE Gujrawala(2017)* - Solve the equation $x(x+7)=(2x-1)(x+4)$ by factorization —
*BISE Sargodha(2015)* - If $\alpha$, $\beta$ are the roots of $3x^2-2x+4=0$, find the values of $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$ —
*BISE Sargodha(2015)* - For what value of $m$ will the roots of the equation $(m+1)x^2+2(m+3)x+m+8=0$ —
*BISE Sargodha(2015)* - Evaluate $(1+w-w^2)(1-w+w^2)$ —
*BISE Sargodha(2016)* - Discuse nature of roots of equation $x^2-5x+6=0$ —
*BISE Sargodha(2016)* - Solve that the roots of $x^2+(mx+c)^2=a^2$ will be equal if $c^2=a^2(1+m^2)$ —
*BISE Sargodha(2016)* - When $x^3+kx^2-7x+6$ is divided by $x+2$ the reminder is $-4$? Find the value of $k$. —
*BISE Lahore(2017)* - Prove that $1+w+w^2=0$ —
*BISE Lahore(2017)* - Solve $3^{2x-1}-12.3^x+81=0$ —
*BISE Lahore(2017)* - When $x^4+2x^3+kx^2+3$ is dividing by $x-2$ the reminder is $1$. Find the value of $k$ —
*FBISE (2016)* - If $\alpha$, $\beta$ are the roots of the equation $5x^2-x-2=0$ then form the equation whose roots are $\frac{3}{\alpha}$ and $\frac{3}{\beta}$. —
*FBISE (2016)* - Show that the roots of the equation $(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0$ are real, also show that the roots will be equal only if $a=b=c$ —
*FBISE (2017)* - Find the values of $a$ and $b$ if $-2$ and $2$ are the roots of the polynomial $x^3-4x^2+ax+b$ —
*FBISE (2017)*