Question

A quartic polynomial f(x) has 2 rational roots at (2, 0) and (-1,0)
and a root at ( - 1+ 3.0). If f(-2) = -2, then what is f(3)?

a. -13/3
b. 13
c. 13/3
d. -13
e. answer is not there​

Answer 1

Answer:

a.-13/3 will answer of this question

Answer 2

The correct question is

A quartic polynomial f(x) has 2 rational roots at (2,0) and (-1,0) and root at (-1±√3,0) if f(-2) is -2, then what is f(3) a) (-13/3) b) (13) c) (13/3) d) -(-13) e)answer is not there

Concept

In algebra, a quartic function is a function of the form f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e, where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

Given

It is given that a quartic polynomial f(x) has 2 rational roots at (2,0) and (-1,0) and root at (-1±√3,0) and f(-2) is -2

Find

We need to find the value of f(3)

Solution

2,-1,-1+√3,-1-√3 are roots of Quartic polynomial

Then Quartic polynomial is given by

f(x) = A (x-2) (x+1) (x+1-√3) (x+1+√3)

f(x)=A (x-2) (x+1) ((x+1)^2 - 3)

f(-2) =A (-2-2) (-2+1) ((-2+1)^2 -3)

-2= A(-4)(-1)(-2)

A=-2/(-8)

A=1/4

Thus, the Quartic polynomial is

f(x)=(1/4) (x-2) (x+1) ((x+1)^2 - 3)

f(3)=(1/4) (3-2) (3+1) ((3+1)^2 -3)

f(3)=(1/4) (1) (4) (13)

f(3)= 13

Hence the value of f(3) is 13

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