Question

Find the zeroes of the quadratic polynomial f(x) = 4x² – 4x – 3 and verify the relation between its zeroes and coefficients.

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

4x² – 4x – 3

Answer 1

We have:

f(x) = 4x² – 4x – 3

= 4x² – (6x – 2x) – 3

= 4x² – 6x + 2x – 3

= 2x(2x – 3) + 1(2x – 3)

= (2x + 1) (2x – 3)

∴ f(x) = 0 ⇒ (2x + 1) (2x – 3) = 0

⇒ 2x + 1 = 0 or 2x – 3 = 0

⇒ `x = (-1)/2` or `x = 3/2` 

So, the zeroes of f(x) are `(-1)/2` and `3/2`. 

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

= `(-1 + 3)/2`

= `2/2`

= 1

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

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

= `(-3)/4`

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