# What are all the possible rational zeros for #f(x)=x^3+x^2-5x+3# and how do you find all zeros?

##### 1 Answer

Nov 23, 2016

1,1, -3

#### Explanation:

Substituting x=1 makes f(x)= 1+1-5+3 =0 hence x=1 is one of the rational zeros.

Since x=1 is a zero, x-1 would be a factor of f(x). therefore divide f(x) by x-1 by using long or synthetic division.

So,

Now for finding other zeros of f(x), put

This quadratic equation can be solved by factorisation or using quadratic formula.

Factorisation is quite easy. Writing 2x as 3x-x, the quadratic expression becomes

(x-1)(x+3)=0 giving x= 1, -3

Thus all the zeros of f(x) are now known. These are, 1( which is a repeated zero) and -3