Question

Find the zeroes of the polynomial r(x) = 4x² + 3x − 1. Hence, write a polynomial whose zeroes are the reciprocals of the zeroes of polynomial r(x).

Answer 1

r(x) = 4x² + 3x − 1

Let, r(x) = 0

4x² + 3x − 1 = 0

4x² + 4x − x − 1 = 0

4x(x + 1) − 1(x + 1) = 0

(x + 1) (4x − 1) = 0

4x − 1 = 0, x + 1 = 0

x = `1/4`, x = − 1

According to question,

New zeroes α = 4, β = −1

Sum of new zeroes = 3, Product of new zeroes = −4

New quadratic equation = (x² − (Sum new zeroes)x + Product new zeroes) = 0

⇒ (x² − 3x − 4) = 0

Hence, the new polynomial is x² − 3x − 4.