Question

The quadratic function g(x)=ax^2+bx+c has the complex roots (-7+4i) and (-7-4i)

Answer 1

Answers:

a = 1

b = 14

c = 65

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Explanation:

Let's focus on the root x = -7+4i

Add 7 to both sides, then square both sides. Then get everything to one side so 0 is on the other side.

x = -7+4i

x+7 = 4i

(x+7)^2 = (4i)^2

(x+7)^2 = 16i^2

(x+7)^2 = 16(-1)

(x+7)^2 = -16

(x+7)^2+16 = 0

If you were to follow those steps for the other root -7-4i, then you should get the same result. Solving (x+7)^2+16 = 0 leads to the two complex roots -7+4i and -7-4i.

Expand out that expression to get it into standard form

(x+7)^2+16

(x+7)(x+7)+16

x^2+7x+7x+49+16

x^2+14x+65

The equation is now in y = ax^2+bx+c form

a = 1

b = 14

c = 65

If you were to plug those a,b,c values into the quadratic formula, you'll find that it leads to the two given roots -7+4i and -7-4i.