Question

Find the zeroes of the polynomial f(x)=x3-3x2-4x+12 if two zeroes are equal in magnitude but opposite in sign

Answer 1

Hope it helps............

Answer 2

f(x) = x³-3x²-4x+12 = 0

x²(x-3)-4(x-3) = 0

(x-3)(x²-4) = 0

(x-3)(x²-2²) = 0

[a²-b² = (a+b)(a-b) }

(x-3)(x+2)(x-2) = 0

(x-3) = 0 ; x = 3

(x+2) = 0 ; x = -2

(x-2) = 0 ; x = 2

Therefore, the zeroes of the given polynomial are 3,2 and -2.

Here, two zeroes which are equal in magnitude but opposite in sign are 2 and -2.

Hope it helps...