Question

find the zeroes of the polynomial if f(x)=2x^3-9x^2+x+12
(find three zeroes)

Answer 1

Answer:

The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.

A real number k is a zero of a polynomial p(x), if p(k)= 0.

Given,

f(x) = 2x3-9x2+x+12

Let x=-1

f(-1) = 2(-1)^3-9(-1)^2+(-1)+12

f(-1)=0

So - 1 is the zero of the polynomial.

Now by further solving the equation using synthetic division method, (shown in picture)

We get,

2x^2-11x+12=0

Solving the above equation,

2x^2-8x-3x+12=0

2x(x-4)-3(x-4)=0

(2x-3)(x-4)=0

x=3/2 or 4

Therefore,

Zeros of the polynomial

f(x) = 2x3-9x2+x+12 are

x=-1 , 3/2 , 4