Question

Find the zeroes of the polynomial q(x) = 8x² − 2x − 3. Hence, find a polynomial whose zeroes are 2 less than the zeroes of q(x).

Answer 1

q(x) = 8x² − 2x − 3

= 8x² + 4x − 6x − 3 = 0

= 4x(2x + 1) − 3(2x + 1) = 0

= (2x + 1) (4x − 3) = 0

Zeroes are x = `(-1)/2, x = 3/4`

New zeroes α = `(-1)/2 - 2 = (-5)/2`

β = `3/4 - 2 = (-5)/4`

Sum of zeroes = `(-15)/4`

Product of zeroes = `25/8`

New polynomial = k[x² − (Sum)x + Product]

= `k(x^2 + 15/4 x + 25/8)`

= 8x² + 30x + 25