Question

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

4x² – 3x – 1

Answer 1

4x² – 3x – 1

Splitting the middle term, we get,

4x² – 4x + 1x – 1

Taking the common factors out, we get,

4x(x – 1) + 1(x – 1)

On grouping, we get,

(4x + 1)(x – 1)

So, the zeroes are,

4x + 1 = 0

`\implies` 4x = – 1

`\implies` x = `(-1/4)`

(x – 1) = 0

`\implies` x = 1

Therefore, zeroes are `(-1/4)` and 1

Verification:

Sum of the zeroes = – (coefficient of x) ÷ coefficient of x²

α + β = `– b/a`

`1 - 1/4 = - (- 3)/4 = 3/4`

Product of the zeroes = constant term ÷ coefficient of x²

αβ = `c/a`

`1(-1/4) = - 1/4`

`-1/4 = -1/4`