Answer:

1,1, -3

Step-by-step 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.

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So,

f

(

x

)

=

(

x

−

1

)

(

x

2

+

2

x

−

3

)

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

x

2

+

2

x

−

3

=

0

and solve for x.

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

2

+

3

x

−

x

−

3

=

0

x

(

x

+

3

)

−

1

(

x

+

3

)

=

0

(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