Question

5
16. Find the quadratic polynomial, the sum of whose zeros is
product is 1. Hence, find the zeros of the polynomial.
and verify

​

Answer 1

Answer:

Given : Sum fo zeroes = (α+β)=0

Product of the zeroes = αβ=−1

Required quadratic polynomial is

x

2

−(α+β)x+αβ=x

2

−(0)x−1

=x

2

−1

Now, find the zeroes of the above polynomial.

Let f(x)=x

2

−1

= x

2

−1

2

=(x−1)(x+1)

Substitute f(x)=0

(x−1)=0 or (x+1)=0

⇒x=1 or x=−1

1 and −1 are the zeroes of the polynomial.