If the roots of the equation ax^2 + bx + c = | vedclass

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

Question

(C) Given that $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$.From the relation between roots and coefficients,we have $\alpha

Vedclass · Accepted Answer

$\frac{1}{\alpha}, \frac{1}{\beta}$

Vedclass · Answer

(C) Given that $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$.From the relation between roots and coefficients,we have $\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$.Let the roots of the equation $cx^2 + bx + a = 0$ be $\alpha'$ and $\beta'$.Then,$\alpha' + \beta' = -\frac{b}{c}$ and $\alpha'\beta' = \frac{a}{c}$.We observe that $\alpha'\beta' = \frac{a}{c} = \frac{1}{c/a} = \frac{1}{\alpha\beta}$.Also,$\alpha' + \beta' = -\frac{b}{c} = \frac{-b/a}{c/a} = \frac{\alpha + \beta}{\alpha\beta} = \frac{1}{\beta} + \frac{1}{\alpha}$.Thus,the roots are $\frac{1}{\alpha}$ and $\frac{1}{\beta}$.

If the roots of the equation $ax^2 + bx + c = 0$ are $\alpha$ and $\beta$,then the roots of the equation $cx^2 + bx + a = 0$ are

Similar Questions

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If one root of the equation $i x^2 - 2(i + 1) x + (2 - i) = 0$ is $(2 - i)$,then the other root is

If $\frac{\alpha}{\alpha+1}$ and $\frac{\beta}{\beta+1}$ are the roots of the quadratic equation $x^2+7x+3=0$,then the equation having roots $\alpha$ and $\beta$ is

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - a(x + 1) - b = 0$,then $(\alpha + 1)(\beta + 1) = $

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x+6=0$,then $\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2$ is equal to :

Vedclass Test Series

Exam Paper Generator

Online Exam Module