Question

if alpha and beta are the zeroes of the polynomial x2-px+q then find the value of alpha3 beta3+alpha2 beta2​

Answer 1

Given :

α, β are the zeroes of x² - px + q

To find :

The value of α³β³ + α²β²

Solution :

Comparing x² - px + q with ax² + bx + c we get,

• a = 1
• b = - p
• c = q

We know that

Product of zeroes = αβ = c / a = q / 1 = q

Now, α³β³ + α²β²

= ( αβ )³ + ( αβ )²

= ( q )³ + ( q ) ²

= q³ + q²

Therefore the value α³β³ + α²β² is q³ + q²

Answer 2

$\tt{\pink{\huge{Hello!!! }}}$

$\tt{ \purple{ \leadsto{f(x) = {x}^{2} - px \: + q}}}$

$\tt{ \orange { \leadsto{ \alpha \beta = \dfrac{c}{a} = q}}}$

${ \alpha }^{3} { \beta }^{3} + { \alpha }^{2} { \beta }^{2} \\ \\ = > { (\alpha \beta) }^{2} ( \alpha \beta + 1) \\ \\ = > {q}^{3} + q$