Question

For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.

`21/8, 5/16`

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) = `x^2 – (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

`\implies` x = `1/8, 5/2`