Use the remainder theorem to determine which number is a root of f(x) = 2x3 + x2 - 7x + 4.

The Roots of f(x) are

x=1

x=

and x=

Step-by-step explanation:

Given function f(x)=

We know that

A. The sum of coefficient of polynomial is zero then, (x-1) is one of root of polynomial

f(1)=0

B. The difference of sum of coefficient of odd term and sum of coefficient of even term of polynomial is zero then, (x+1) is one of root of polynomial

f(-1)=0

Let x=1

f(1)=

f(1)=2+1-7+4=0

Therefore, (x-1) is one of root.

Let x=(-1)

f(1)=

f(1)=-2+1+7+4=10

Therefore, (x-1) is not one of root.

Using Remainder theorem:

Dividing (x-1) on both the side.

For 2x^{2}+3x-4

a=2,b=3 and c=(-4)

D=

D=

D=

x= and x=

x= and x=

x= and x=

Thus,

The Roots of f(x) are

x=1

x=

and x=