If alpha and beta are the roots of the equati | vedclass

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

Question

(B) Given the equation $x^2 + px + q = 0$ with roots $\alpha$ and $\beta$.We know that $\alpha + \beta = -p$ and $\alpha \beta = q$.Let the new roots

Vedclass · Accepted Answer

$x^2 + px + q = 0$

Vedclass · Answer

(B) Given the equation $x^2 + px + q = 0$ with roots $\alpha$ and $\beta$.We know that $\alpha + \beta = -p$ and $\alpha \beta = q$.Let the new roots be $\alpha' = q/\alpha$ and $\beta' = q/\beta$.The sum of the new roots is $\alpha' + \beta' = \frac{q}{\alpha} + \frac{q}{\beta} = q \left( \frac{\alpha + \beta}{\alpha \beta} ight) = q \left( \frac{-p}{q} ight) = -p$.The product of the new roots is $\alpha' \beta' = \left( \frac{q}{\alpha} ight) \left( \frac{q}{\beta} ight) = \frac{q^2}{\alpha \beta} = \frac{q^2}{q} = q$.The required equation is $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^2 - (-p)x + q = 0$,which simplifies to $x^2 + px + q = 0$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + px + q = 0$,then what is the equation whose roots are $q/\alpha$ and $q/\beta$?

Similar Questions

If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0$,then the value of $\alpha^6+\beta^6$ is

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is

If $f(x) = 2x^3 + mx^2 - 13x + n$ and $2, 3$ are the roots of the equation $f(x) = 0$,then the value of $4m + 5n$ is:

The value of $a$ for which one root of the quadratic equation $(a^2 - 5a + 3)x^2 + (3a - 1)x + 2 = 0$ is twice as large as the other,is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^{3}+4x+2=0$,then $\alpha^{3}+\beta^{3}+\gamma^{3}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module