Question

7.Find the value of a and b so that x+1 and x-1 are factors of x4 +ax3 +2x2 -3x+b.

Answer 1

Answer:

The value of $a$ and $b$ are $3$ and $-3$ respectively.

Step-by-step explanation:

In general, if $(x+a)$ is a factor of a polynomial $P(x)$, then $P(a)=0$ .

Given the polynomial

$P(x)=x^4+ax^3+2x^2-3x+b$

Since $x+1$ and $x-1$ are  factors of the polynomial, we have

$P(-1)=0\\P(1)=0$

Then it follows that,

$P(-1)=0 \\\\\implies (-1)^4+a(-1)^3+2(-1)^2-3(-1)+b=0\\\\\implies 1-a+2+3+b=0\\\\\implies 6-a+b=0$

Also,

$P(1)=0\\\\\implies 1^4+a\times 1^3+2\times 1^2-3\times 1+b=0\\\\\implies 1+a+2-3+b=0\\\\\implies a+b=0$

From these equations, we get,

$\implies 6+2b=0\\\\\implies 2b=-6\\\\\implies b=\dfrac{-6}{2}=-3$

So

$a=3$

The value of $a$ and $b$ are $3$ and $-3$ respectively.