Find all the zeros of the quadratic function.

If there is more than one zero, separate them with commas.
If there are no zeros, click on “None”.

Question

Find all the zeros of the quadratic function. $$ y=x^{2}+7 x-30 $$ If there is more than one zero, separate them with commas. If there are no zeros, click on "None".

UpStudy AI · Accepted Answer

We start with the quadratic function
$$
y=x^2+7x-30.
$$

**Step 1. Factor the quadratic**

Look for two numbers that multiply to $$-30$$ (the product of the coefficient of $$x^2$$ which is $$1$$ and the constant $$-30$$) and add to $$7$$ (the coefficient of $$x$$). The numbers $$10$$ and $$-3$$ satisfy these conditions because
$$
10 \times (-3) = -30 \quad \text{and} \quad 10 + (-3) = 7.
$$

**Step 2. Write the factored form**

Write the quadratic as
$$
x^2+7x-30 = (x+10)(x-3).
$$

**Step 3. Find the zeros**

Set each factor equal to zero:
$$
x+10 = 0 \quad \Longrightarrow \quad x = -10,
$$
$$
x-3 = 0 \quad \Longrightarrow \quad x = 3.
$$

Thus, the zeros of the function are 
$$
x = -10, \quad x = 3.
$$
The zeros of the function are $$ x = -10 $$ and $$ x = 3 $$.

Find all the zeros of the quadratic function.

If there is more than one zero, separate them with commas.
If there are no zeros, click on “None”.

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Find all the zeros of the quadratic function. If there is more than one zero, separate them with commas. If there are no zeros, click on “None”.

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Latest Algebra Questions

Find all the zeros of the quadratic function.

If there is more than one zero, separate them with commas.
If there are no zeros, click on “None”.