Question

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

Answer 1

Zeroes, or x-intercepts, are x = `4/5` and `-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=25x^2+10x-24`

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

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

Step 3: Factor!
`(-5x+4)(5x+6)`

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

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

`x=4/5` and `-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]}