Question

If one root of equation 2x ^ 2 + x + k = 0is - 2 . Find the value of k and the other root
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Answer 1

Resposta:

Good morning!

If one root is -2, then x = -2:

2x² + x + k = 0

2(-2)² + 2 + k = 0

2*4 + 2 + k = 0

8 + 2 + k = 0

k = -8 - 2

k = -6

So the equation is:

2x² + x - 6 = 0

a = 2 ; b = 1 ; c = -6

Δ = b² - 4ac

Δ = 1 - 4*2*(-6)

Δ = 1 + 48

Δ = 49

√Δ = √49 = 7

x = (-b ± √Δ) / 2a

x = (-1±7)/2*2

x = -2 is the negative root. The positive one is:

x = (-1+7)/4

x = 6/4

x = 3/2