Question

Find value of k in x^2-6x+k if its a and b are its zeroes and a^2+b^2=40.

Answer 1

Heya

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

Given, a and b are zeroes

Hence, sum of zeroes are :
$a + b = 6$
Also, given :
${a}^{2} + {b}^{2} = 40$
We know :
${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

$= > 36 = 40 + 2ab$
$= > k = ab = - 2$