Question

if alpha and beta are zeros of the polynomial x² - 6 X + k find k such that (alpha+beta)²-2alha beta =40​

Answer 1

k = - 2

Explanation:

Given α and β are the zeros of x² - 6x + k = 0 , with

a = 1, b = - 6 and c = k , then

α + β = -
`(b)/(a)` = -
`(-6)/(1)` = 6

αβ =
`(c)/(a)` =
`(k)/(1)` = k

Then solving

(α + β)² - 2αβ = 40

6² - 2k = 40

36 - 2k = 40 ( subtract 36 from both sides )

- 2k = 4 ( divide both sides by - 2 )

k = - 2