a) Find all the zeros (real or complex) of `f(x)=x^3+2x-3` .

2 Answers

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lemjay | High School Teacher | (Level 3) Senior Educator

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To find the zeros of the function, factor the right side by grouping.
To do so, break down the middle term using the factors of the constant -3.

Since -3 is equal -1*3 and -1+3=2, the middle term can be replaced with -x and 3x.



Then, group the terms into two.


Factor out the GCF in each group.



Then, factor out the GCF of the two groups.



Now that the function is in factor form, set f(x) equal to zero.


To solve for the values of x, set each factor to zero.

For the first factor,




For the second factor, since it is a quadratic expression, apply the quadratic formula.




Hence, the roots of f(x) are `1` , `(-1+isqrt11)/2` and `(-1-isqrt11)/2` .