Quadratic Zero Equations Sample Problems

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Quadratic Zero Equations

For this topic, you will need to know how to factor polynomials.
To review factoring, see Trinomial Factoring.

In this topic, you will solve polynomial equations set to equal 0. This can also be called finding the roots or zeros.
The zero or root of a polynomial P(x) is a value that makes P(x) = 0.

x² - 6x + 8
When x = 2 or x = 4, the polynomial equals 0.
So 2 and 4 are zeros or roots of the polynomial.

Example 1:

Factor the expression and solve for the zeros. Write answers in ascending order, separated by commas. Example: x=-3/2,2;
3x³ - 6x² - 9x = 0
x =
1. Factor the polynomial.

3x³ - 6x² - 9x = 0

3x(x² - 2x - 3) = 0

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

2. Set each factor to equal 0 and solve.

3x = 0

x = 0

x + 1 = 0

x = -1

x - 3 = 0

x = 3

So the answer is x =