Question

if alpha and beta are the zeroes of p(x)=x2-8x+k and alpha2 +beta2=40 then findthe value of k

Answer 1

Hola Friend ✋✋✋

p(x) = x² - 8x + k

Let 'a' be alpha and 'b' be beeta

a + b = 8

ab = k

a² + b² = 40

( a + b )² = 8²

a² + b² + 2ab = 64

40 + 2k = 64

2k = 24

k = 12

Hope it helps

Answer 2

HELLO DEAR,

GIVEN THAT:-



$given \\ { \alpha }^{2} + { \beta }^{2} = 40................(1)$




$\alpha + \beta = - \frac{( -b )}{a} \\ \alpha + \beta = - \frac{ (-8 )}{1} \\ = > \alpha + \beta = 8 ..............(2)\\ = > \alpha \times \beta = \frac{c}{a} \\ = > \alpha \times \beta = k.................(3) \\ = > ( \alpha + \beta )^{2} = {8}^{2} ...using(2) \\ = > { \alpha }^{2} + { \beta }^{2} + 2 \alpha \beta = 64 \\ = > { \alpha }^{2} + { \beta }^{2} = 64 - 2k......using(3) \\ = > 40 = 64 - 2k........from(1) \\ = > 2k = 64 - 40 \\ = > 2k = 24 \\ = > k = \frac{24}{2} = 12$


I HOPE ITS HELP YOU DEAR,
THANKS