Find the quadratic polynomial, sum of whose zeroes is 8 and their prod

1.	Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
Answer» Given : Sum of zeroes = (∝ + β) = 8 Product of the zeroes = = 12 Required quadratic polynomial is x² – (∝+β)x + ∝β = x² – (8)x + 12 Now, find the zeroes of the above polynomial. Let f(x) = x² – (8)x + 12 = x² – 6x – 2x + 12 = (x -6)(x – 2) Substitute f(x) = 0. either (x -6) = 0 or (x – 2) = 0 x = 6 or x = 2 2 and 6 are the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

Answer»

Given : Sum of zeroes = (∝ + β) = 8

Product of the zeroes = = 12

Required quadratic polynomial is

x² – (∝+β)x + ∝β

= x² – (8)x + 12

Now, find the zeroes of the above polynomial.

Let f(x) = x² – (8)x + 12

= x² – 6x – 2x + 12

= (x -6)(x – 2)

Substitute f(x) = 0.

either (x -6) = 0 or (x – 2) = 0

x = 6 or x = 2

2 and 6 are the zeroes of the polynomial.