Question

Write the zeros of the polynomial x² – x – 6.

Answer 1

We have to find the zeros of the polynomial `x^2 - x - 6`

`f(x)= x^2 - x-6`

`f(x)= x^2 - 3x + 2x -6`

`f(x) = x(x-3)+2 (x-3)`

`f(x) = (x + 2) (x - 3)`

We know that if `(x - a)` is a factor of f(x) then x = a is a zero of polynomial

Therefore we have

`x + 2 = 0`

` x = -2`

Also

` x - 3 = 0 `

`x = 3 `

Hence, the zeros of polynomial `x^2 - x- 6` is `3, -2`.