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 properties of quadratic equations,we have:$\alpha + \be

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 properties of quadratic equations,we have:$\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$.Now,consider the equation $cx^2 + bx + a = 0$. Let its roots be $\alpha'$ and $\beta'$.For this equation,the sum of roots is $\alpha' + \beta' = -\frac{b}{c}$ and the product of roots is $\alpha'\beta' = \frac{a}{c}$.We can express the sum of the reciprocals of the original roots as:$\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha\beta} = \frac{-b/a}{c/a} = -\frac{b}{c}$.Also,the product of the reciprocals is:$\frac{1}{\alpha} \cdot \frac{1}{\beta} = \frac{1}{\alpha\beta} = \frac{1}{c/a} = \frac{a}{c}$.Since the sum and product of the roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ match the sum and product of the roots of the equation $cx^2 + bx + a = 0$,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

If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-3 \lambda x+\lambda^{2}=0,$ find $\lambda$ if $\alpha^{2}+\beta^{2}=\frac{7}{4}$

Solve the given two equations and choose the correct option.
$I.$ $2x^{2} - 13x + 21 = 0$
$II.$ $5y^{2} - 22y + 21 = 0$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt[3]{4913}$
$II.$ $13y + 3x = 246$

The roots of the equation $x^2 + bx - c = 0$ where $b, c > 0$ are:

Solve the given two equations and select the correct option.
$I. 3x^2 + 5x - 2 = 0$
$II. 2y^2 - 7y + 5 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module