Question

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

`2x^2 + (7/2)x + 3/4`

Answer 1

`2x^2 + (7/2)x + 3/4`

The equation can also be written as,

8x² + 14x + 3

Splitting the middle term, we get,

8x² + 12x + 2x + 3

Taking the common factors out, we get,

4x(2x + 3) + 1(2x + 3)

On grouping, we get,

(4x + 1)(2x + 3)

So, the zeroes are,

4x + 1 = 0

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

2x + 3 = 0

`\implies` x = `-3/2`

Therefore, zeroes are `-1/4` and `-3/2`

Verification:

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

α + β = `- b/a`

`(-3/2) + (-1/4) = - (7)/4`

= `-7/4` 

Product of the zeroes = constant term ÷ coefficient of x²

αβ = `c/a`

`(-3/2)(-1/4) = (3/4)/2`

= `3/8`