Question

If 2-i is a root of the equation ax2 + 12x + b = 0) (where a and b are real), then the value of ab is equal to
(A) 45
(B)-45
(C) 20
(D) √3
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Answer 1

Step-by-step explanation:

I’ll assume you’re solving ax^2 + 12x + b = 0

Complex roots of quadratics always come in conjugate pairs, meaning we know the other root is 2+i

x = 2 +- i

x-2 = +- i

(x-2)^2 = -1

x^2 -4x + 4 = -1

x^2 - 4x + 5 = 0

-3x^2 + 12x - 15 = 0

Which means a = -3, b = -15 and ab = 45