Question

If alpha and beta are zeros of polynomial x2+px+q ,form a polynomial whoese zeros are alpha plus beta squere and alpha minus beta square

Answer 1

hope this would help you

Answer 2

Answer:

$x^2 - (2p^2 - 4q)x + p^4 - 4p^2q$

Step-by-step explanation:

Given polynomial,

$x^2 + px + q$

If $\alpha$ and $\beta$ are the roots of the polynomial, then,

$\alpha + \beta = -\frac{p}{1}= -p$

$\alpha.\beta =\frac{q}{1}= q$

$\implies (\alpha + \beta )^2 = (-p)^2 = p^2$

$(\alpha - \beta )^2 =   (\alpha + \beta )^2 - 4\alpha.\beta = p^2-4q$

Since, if a and b are the roots of a quadratic equation the the equation is,

$x^2 - (a+b)x + ab = 0$

Thus, the required equation,

$x^2 - (p^2 + p^2 - 4q)x + p^2(p^2 - 4q)$

$x^2 - (2p^2 - 4q)x + p^4 - 4p^2q$