# How do you find the zeros of f(x)=25x^2+10x-24?

Feb 28, 2017

Zeroes, or x-intercepts, are x = $\frac{4}{5}$ and $- \frac{6}{5}$

#### Explanation:

When a math problem asks to find the "zeroes" of the equation, it is asking for the x-intercepts of the equation. In other words, you must set the equation equal to zero.

Step 1: Set it equal to zero
$0 = 25 {x}^{2} + 10 x - 24$

Step 2: Move the equation to the left side by subtracting $25 {x}^{2} + 10 x - 24$

You're left with:
$- 25 {x}^{2} - 10 x + 24 = 0$

Step 3: Factor!
$\left(- 5 x + 4\right) \left(5 x + 6\right)$

Step 4: Set each side equal to zero.
$- 5 x + 4 = 0$
$5 x + 6 = 0$

Step 5: Solve until $x$ is alone on the left side.

$x = \frac{4}{5}$ and $- \frac{6}{5}$

Note: You can also double check by graphing and looking at the x-intercepts!
graph{y=25x^2+10x-24 [-7.9, 7.9, -3.95, 3.95]}