Question

A parabola of the form y=2x^2+bx+c has complex roots of -1 plus/minus 4i. Find the values of b and c.

help asap please and thank you!!!

Answer 1

• b = 4
• c = 34

Explanation:

The sum of the two roots is ...

(-1 +4i) + (-1 -4i) = -2

This value is the opposite of b/2, so b = -2(-2) = 4.

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The product of the two roots is ...

(-1 +4i)(-1 -4i) = ((-1)² -(4i)²) = 1 +16 = 17

This value is c/2, so c = 2(17) = 34.

The value of b is 4; the value of c is 34.

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Further explanation

A quadratic factored as ...

y = a(x -p)(x -q)

expands to ...

y = ax^2 -a(p+q)x +apq

So, for roots p and q, ...

b = -a(p+q)

c = apq

In this problem , a=2, p=-1+4i, q=-1-4i.