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

Mar 20, 2018

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

#### Explanation:

Given: $y = 5 {x}^{2} - 2$

Set $y = 0$:

$0 = 5 {x}^{2} - 2$

Flip the equation:

$5 {x}^{2} - 2 = 0$

Add 2 to both sides:

$5 {x}^{2} = 2$

Divide both sides by 5:

${x}^{2} = \frac{2}{5}$

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

$x = - \sqrt{\frac{2}{5}}$ and $x = \sqrt{\frac{2}{5}}$

Multiply both by 1 in the form of $\frac{5}{5}$:

$x = - \sqrt{\frac{2}{5} \frac{5}{5}}$ and $x = \sqrt{\frac{2}{5} \frac{5}{5}}$

$x = - \sqrt{\frac{10}{25}}$ and $x = \sqrt{\frac{10}{25}}$

$x = - \frac{\sqrt{10}}{5}$ and $x = \frac{\sqrt{10}}{5}$

Check that both values produce $y = 0$:

$y = 5 {\left(- \frac{\sqrt{10}}{5}\right)}^{2} - 2$ and $y = 5 {\left(- \frac{\sqrt{10}}{5}\right)}^{2} - 2$

$y = \frac{10}{5} - 2$ and $y = \frac{10}{5} - 2$

$y = 2 - 2$ and $y = 2 - 2$

$y = 0$ and $y = 0 \leftarrow$ this checks

The zeros are $x = - \frac{\sqrt{10}}{5} \mathmr{and} x = \frac{\sqrt{10}}{5}$

Mar 20, 2018

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

#### Explanation:

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

$5 {x}^{2} - 2 = 0$

Add 2 to both sides to get:
$5 {x}^{2} = 2$

Then, divide both sides by 5:
${x}^{2} = \frac{2}{5}$

Then, take the square root of both sides:
$\sqrt{{x}^{2}} = \sqrt{\frac{2}{5}}$

The final answer is:
$x = + \sqrt{\frac{2}{5}}$ and $- \sqrt{\frac{2}{5}}$