If alpha, beta are the roots of the equation | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that $\alpha, \beta$ are the roots of $Ax^2 + Bx + C = 0$. From the relation between roots and coefficients,$\alpha + \beta = -B/A$ and $\al

Vedclass · Accepted Answer

$\frac{2AC - B^2}{A^2}$

Vedclass · Answer

(B) Given that $\alpha, \beta$ are the roots of $Ax^2 + Bx + C = 0$. From the relation between roots and coefficients,$\alpha + \beta = -B/A$ and $\alpha\beta = C/A$. Given that $\alpha^2, \beta^2$ are the roots of $x^2 + px + q = 0$. From the relation between roots and coefficients,$\alpha^2 + \beta^2 = -p$ and $\alpha^2\beta^2 = q$. We know that $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$. Substituting the values,$-p = (-B/A)^2 - 2(C/A)$. $-p = \frac{B^2}{A^2} - \frac{2C}{A} = \frac{B^2 - 2AC}{A^2}$. Therefore,$p = -\frac{B^2 - 2AC}{A^2} = \frac{2AC - B^2}{A^2}$.

If $\alpha, \beta$ are the roots of the equation $Ax^2 + Bx + C = 0$ and $\alpha^2, \beta^2$ are the roots of the equation $x^2 + px + q = 0$,then $p = \dots$

Similar Questions

If $\alpha, \beta$ are the roots of the quadratic equation $x^{2}+a x+b=0, (b \neq 0),$ then the quadratic equation whose roots are $\alpha-\frac{1}{\beta}$ and $\beta-\frac{1}{\alpha}$ is:

If $a$ and $b$ are the roots of the equation $y^2+y+1=0$,then the value of $a^4+b^4+a^{-1}b^{-1}$ is

If $A$ is the $A.M.$ of the roots of the equation $x^2 - 2ax + b^2 = 0$ and $G$ is the $G.M.$ of the roots of the equation $x^2 - 2bx + a^2 = 0,$ then

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

If the Arithmetic Mean ($A$.$M$.) and Geometric Mean ($G$.$M$.) of the roots of a quadratic equation in $x$ are $p$ and $q$ respectively,then the equation is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module