Question

If alpha and beta are the zeroes of the poly. x2-6x+k find the value of k such that alpha2 +beta2=40

Answer 1

HELLO DEAR,

X² -6X+K=0

we know that:-

$\alpha + \beta = \frac{ - b}{a} \\ and \\ \alpha \times \beta = \frac{c}{a}$
$\alpha + \beta = \frac{ - ( - 6)}{1} \\ = \alpha + \beta = 6.....(1) \\ and \\ \alpha \times \beta = \frac{k}{1} \\ = \alpha \times \beta = k.........(2)$
given the:-

${ \alpha }^{2} + { \beta }^{2} = 40$
we also write like that:-

${ \alpha }^{2} + { \beta }^{2} + 2 \alpha \times \beta - 2 \alpha \times \beta = 40 \\ = > {( \alpha + \beta )}^{2} = 40 + 2 \alpha \times \beta \\ = > {( \alpha + \beta )}^{2} = 40 + 2k......using(2) \\ \\ = > {6}^{2} = 40 + 2k.......using(2) \\ \\ = > 2k = 36 - 40 \\ = > k = \frac{ - 4}{2} \\ = > k = - 2$
I HOPE ITS HELP YOU DEAR,
THANKS