Question

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

`4x^2 + 5sqrt(2)x - 3`

Answer 1

Let p(x) = `4x^2 + 5sqrt(2)x - 3`

= `4x^2 + 6sqrt(2)x - sqrt(2)x - 3`

= `2sqrt(2)x (sqrt(2)x + 3) - 1(sqrt(2)x + 3)`

= `(sqrt(2)x + 3)(2sqrt(2)x – 1)`

So, the zeroes of p(x) = `- 3/sqrt(2)` and `1/(2sqrt(2))`

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

= `- 5/(2sqrt(2))`

= `(-5sqrt(2))/4`

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

And product of zeroes = `- 3/sqrt(2) . 1/(2sqrt(2)) = - 3/4`

= `"constant  term"/("coefficient  of"  x^2)`