How do you find the zeros for y=5x^2-2?

2 Answers
Mar 20, 2018

You set y equal 0, then solve the resulting equation for the value(s) of x.

Explanation:

Given: y=5x^2-2

Set y = 0:

0 =5x^2-2

Flip the equation:

5x^2-2= 0

Add 2 to both sides:

5x^2=2

Divide both sides by 5:

x^2=2/5

When we perform the square root operation on both sides, we obtain a negative value and a positive value:

x=-sqrt(2/5) and x=sqrt(2/5)

Multiply both by 1 in the form of 5/5:

x=-sqrt(2/5 5/5) and x=sqrt(2/5 5/5)

x=-sqrt(10/25) and x=sqrt(10/25)

x=-sqrt10/5 and x=sqrt10/5

Check that both values produce y = 0:

y=5(-sqrt10/5)^2-2 and y=5(-sqrt10/5)^2-2

y=10/5-2 and y=10/5-2

y=2-2 and y=2-2

y=0 and y=0 larr this checks

The zeros are x = -sqrt10/5 and x = sqrt10/5

Mar 20, 2018

To find the answer, set up the problem so 5x^2-2=0.

Explanation:

To find the answer, set up the problem so 5x^2-2=0. Then, move everything to one side of the equation, so x is by itself.

5x^2-2=0

Add 2 to both sides to get:
5x^2=2

Then, divide both sides by 5:
x^2=2/5

Then, take the square root of both sides:
sqrt(x^2)=sqrt(2/5)

The final answer is:
x=+sqrt(2/5) and -sqrt(2/5)