Question

Find a quadratic polynomial, the sum and product of whose zeroes are 21/8 and 5/16, respectively. Also find its zeroes.

Answer 1

Sum of the zeroes = 21/8

Product of the zeroes = 5/16

P(x) = x² – (sum of the zeroes) + (product of the zeroes)

Then, P(x)= x² – 21x/8 + 5/16

P(x)= 16x² – 42x + 5

Using splitting the middle term method,

16x² – 42x + 5 = 0

16x² – (2x + 40x) + 5 = 0

16x² – 2x – 40x + 5 = 0

2x (8x – 1) – 5(8x – 1) = 0

(8x – 1)(2x – 5) = 0

⇒ x = 1/8, 5/2