Question

Find the zeroes of the polynomial p(x) = 4x² – 4x – 3 and verify the relationship between zeroes and its coefficients.

Answer 1

4x² – 4x – 3

= 4x² – 6x + 2x – 3

= 2x(2x – 3) + 1(2x – 3)

= (2x – 3) (2x + 1)

Zeroes = `3/2` and `(-1)/2`

Sum of zeroes = `3/2 + ((-1)/2) = 1`

= `(-("Coefficient of"  x))/("Coefficient of"  x^2)`

= `(-(-4))/4`

= 1

Product of zeroes = `3/2 xx (-1)/2 = (-3)/4`

= `"Constant term"/("Coefficient of"  x^2)`

= `(-3)/4`