Question

One zero of f(x)=x^3-2x^2-5x+6 is 1 what are other zeros of the function

Answer 1

-2 and 3

Explanation:

Given one zero of f(x)=x^3-2x^2-5x+6 to be 1 this means that x-1 is a factor of the polynomial x³-2x²-5x+6

Before we can get the other two factors. We need to divide the polynomial function by x-1 and factorize the resulting quotient as shown in the attachment.

Quotient Q(x) = x²-x-6

Factorizing this function

x²-3x+2x-6 = 0

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

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

x+2 = 0 and x-3 = 0

x = -2 and x= 3

Therefore the other zeros of the function are -2 and 3

Answer 2

The other zeros are -2 and 3.

Explanation:

As 1 is a zero then (x - 1) is a factor so we divide:

x - 1 )x^3-2x^2-5x+6(x^2-x-6

x^3-x^2

-x^2-5x

-x^2+x

-6x+6

-6x+6

...........

x^2 - x - 6 = 0

(x - 3)(x + 2)

x = -2, 3.