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

1 Answer
Feb 28, 2017

Answer:

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]}