Question

How do you find all the zeros of `f(x) = 3x^2 − 4x − 15`?

Answer 1

Zeros of `f(x)` are `x=3 and x= -5/3`

Explanation:

`f(x)=3x^2-4x-15 =3x^2-9x+5x-15`

`=3x(x-3)+5(x-3)= (x-3)(3x+5)`

Zeros of `f(x)` are `x=3 and x= -5/3` [Ans]

Answer 2

`x=3,(-5)/3`

Explanation:

Using trial and error method `(x-3)` is a factor of `f(x)`
I.e`(x-3), x=3`
`f(3)=3(3^2)-4(3)-15`
`=3(9)-12-15`
`=27-12-15`
`=0`
Using long division of polynomial's
`(+)3x+5`
`root(x-3)(3x^2-4x-15)`
`((-)3x^2-9x)/(5x-15)`
`((-)5x-15)/(……)`
Since `x` is in the 2nd degree, the 2 factors of `f(x)`are `(x-3)` and `3x+5`
Equating factor to zero.
`x-3=0,3x+5=0`
`x=3,3x=-5`
`x=3,x=(-5)/3`(`color (blue) (zero's. Of.f(x))`)