Question

What are all the rational zeros of `x^3-7x-6`?

Answer 1

Zeros are `x=-1, x=-2 and x=3`

Explanation:

`f(x)=x^3-7 x - 6 ;` By inspection `f(-1)=0` ,so

`(x+1)` will be a factor.

`x^3-7 x - 6 = x^3 + x^2 -x^2 -x -6 x -6`

`= x^2(x + 1) -x(x+1) -6( x +1)`

`= (x + 1)(x^2 -x -6)= (x + 1)(x^2 -3 x +2 x-6)`

`= (x + 1){x(x -3)+2( x-3)}`

`:. f(x)= (x + 1)(x -3)(x+2) :. f(x)` will be zero

for `x=-1, x=-2 and x=3`

Hence zeros are `x=-1, x=-2 and x=3` [Ans]