Question

If x^3+2x^2+ax+b has factors x+1 and x-1, then find a and b

Answer 1

Answer:

f(1) and f(−a) both are equal to 0 by factor theorem.

∴ f(1)=1+2+a+b=0 and f(−a)=−a

3

+2a

2

−a

2

+b=0

∴ a+b=−3 and −a

3

+a

2

+b=0

Thus, on solving two equations we get, a=−1 and b=−2

Answer 2

Answer:

$\huge{\boxed{\rm{\red{a=-1,b=-2}}}}$

Step-by-step explanation:

Given:-

x³+2x²+ax+b has factors x+1 and x-1,

To find:-

Find the values of a and b

Solution:-

Given polynomial p(x)=x³+2x²+ax+b

and given factors are (x+1) and (x-1)

Using concept:-

Factor theorem:-

Let p(x) be a polynomial of degree greater than or equal to 1 and x-a is another linear polynomial then,p(a)= then (x-a) is a factor vice versa.

Now ,If (x+1) and(x-1) are the factors then

p(-1)=0 and p(1)=0

p(-1)=(-1)³+2(-1)²+a(-1)+b=0

=>-1+2-a+b=0

=>1-a+b=0

=>-a+b=-1

=>a-b=1

=>a=1+b-----(1)

and p(1)=(1)³+2(1)²+a(1)+b=0

=>1+2+a+b=0

=>3+a+b=0

=>3+1+b+b=0(from1)

= 4+2b=0

=>2b=-4

=>b=-4/2

=>b=-2

from(1)

=>a=1+(-2)

=>a=1-2

=>a=-1

Answer:-

Values of

a=-1

b=-2