Question

Qs 4 (1) - ii]
Step by step explanation

Answer 1

Step-by-step explanation:

Given,

$\alpha + \beta = 5 \: \: and \: \: { \alpha }^{3} + { \beta }^{3} = 35$

On expanding α³+β³,we get,

$( \alpha + \beta )( { \alpha }^{2} - \alpha \beta + \beta^{2} ) = 35$

$( \alpha + \beta )(( \alpha + \beta )^{2} - 3 \alpha \beta ) = 35$

as we know that (a+b)²=a²+b²+2ab

$= 5(25 - 3 \alpha \beta ) = 35$

putting the value of (α+β),

on solving,we get,

$= \alpha \beta = 6$

Now, we know, a quadratic equation whose roots are α & β, are of the form

k[ x²- (α+β)x + αβ], where k is a constant, belongs to R

so,

$required \: \: quadratic \: \: equation\: \: is \: k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta )$

$= k( {x}^{2} - 5x + 6)$

Hope this will help you..!