Question

Find the zeroes of the polynomial p(x) = 3x² − 4x − 4. Hence, write a polynomial whose each of the zeroes is 2 more than the zeroes of p(x).

Answer 1

3x² − 4x − 4

3x² − 6x + 2x − 4 = 0

3x(x − 2) + 2(x − 2) = 0

(3x + 2) (x − 2) = 0

x = `-2/3`, x = 2 (Zero)

Let the new zeroes be α and β.

α = `-2/3 + 2`, β = 2 + 2

α = `4/3` and β = 4

New quadratic equation,

x² − (α + β)x + α × β = 0

But α + β = `16/3`, α × β = `16/3`

`x^2 - 16/3x + 16/3 = 0`

3x² − 16x + 16 = 0

New polynomimal is 3x² − 16x + 16.