Find the quadratic polynomial, sum of whose zeroes is 0 and their prod

1.	Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial.
Answer» Given : Sum of zeroes = (∝ + β) = 0 Product of the zeroes = = -1 Required quadratic polynomial is x² – (∝+β)x + ∝β = x² – (0)x – 1 = x² – 1 Now, find the zeroes of the above polynomial. Let f(x) = x² – 1 = x² – 1² = (x – 1)(x + 1) Substitute f(x) = 0. either (x – 1) = 0 or (x + 1) = o x = 1 or x = -1 1 and -1 are the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial.

Answer»

Given : Sum of zeroes = (∝ + β) = 0

Product of the zeroes = = -1

Required quadratic polynomial is

x² – (∝+β)x + ∝β

= x² – (0)x – 1

= x² – 1

Now, find the zeroes of the above polynomial.

Let f(x) = x² – 1

= x² – 1²

= (x – 1)(x + 1)

Substitute f(x) = 0.

either (x – 1) = 0 or (x + 1) = o

x = 1 or x = -1

1 and -1 are the zeroes of the polynomial.