Question

Q1.Write the common zero of the polynomials.x^3 + x^2 - 1 and x^2+ 2x + 1.​

Answer 1

Explanation:

Given

x³+x²-1 and x²+2x+1

To Find

we have to find the common zeroes

SOLUTION:

Let p(x) = x³+x²-1

and q(x)= x²+2x+1

p(x)= x³+x²-1= x²( x+1)-1

q(x)= x²+2x+1= x( x-2) +1

p(x)= (x+1)(x²-1)

Identity used : a²-b²= (a+b)(a-b)

p(x)=>(x+1)(x+1)(x-1)

q(x)= (x-2)(x+1)

on putting p(x)= 0

we get x= -1 and x= 1

on putting q(x)=0

we get x= 2 and x= -1

Since , -1 is common in both

so,

The common zeroes of the polynomial x³+x²-1

and x²+2x+1 is (x+1) or x= -1

Answer 2

Given:-

x³+x²-1 and x²+2x+1

To Find

we have to find the common zeroes

Solution:-

Let p(x) = x³+x²-1

and q(x)= x²+2x+1

p(x)= x³+x²-1= x²( x+1)-1

q(x)= x²+2x+1= x( x-2) +1

p(x)= (x+1)(x²-1)

Identity used : a²-b²= (a+b)(a-b)

p(x)=>(x+1)(x+1)(x-1)

q(x)= (x-2)(x+1)

on putting p(x)= 0

we get x= -1 and x= 1

on putting q(x)=0

we get x= 2 and x= -1

Since , -1 is common in both

so,

The common zeroes of the polynomial x³+x²-1

and x²+2x+1 is (x+1) or x= -1