Question

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

3x² + 4x – 4

Answer 1

3x² + 4x – 4

Splitting the middle term, we get,

3x² + 6x – 2x – 4

Taking the common factors out, we get,

3x(x + 2) – 2(x + 2)

On grouping, we get,

(x + 2)(3x – 2)

So, the zeroes are,

x + 2 = 0

`\implies` x = – 2

3x – 2 = 0

`\implies` 3x = 2

`\implies` x = `2/3`

Therefore, zeroes are `(2/3)` and – 2

Verification:

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

α + β = `– b/a`

`-2 + (2/3) = - (4)/3`

= `- 4/3 = -4/3`

Product of the zeroes = constant term ÷ coefficient of x²

αβ = `c/a`

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