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2 years ago

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

Mathematics

1 answer:

lidiya [134]2 years ago

8 0

Answer:

k = - 2

Step-by-step explanation:

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

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

α + β = - $\frac{b}{a}$ = - $\frac{-6}{1}$ = 6

αβ = $\frac{c}{a}$ = $\frac{k}{1}$ = 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

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

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