What are the roots of y = x2 – 3x – 10?

–3 and –10
–2 and 5
2 and –5
3 and 10

To find the roots of the quadratic equation \( y = x^2 - 3x - 10 \), we can factor the equation and solve for \( x \).

The quadratic equation is:

\[
x^2 - 3x - 10 = 0
\]

We need to find two numbers that multiply to give \(-10\) and add to give \(-3\). These numbers are \(-5\) and \(2\), because:

\[
(-5) \times (2) = -10 \quad \text{and} \quad (-5) + 2 = -3
\]

Thus, we can factor the quadratic as:

\[
(x - 5)(x + 2) = 0
\]

Now, solve for \(x\):

\[
x - 5 = 0 \quad \text{or} \quad x + 2 = 0
\]

So:

\[
x = 5 \quad \text{or} \quad x = -2
\]

Thus, the roots of the equation are \( x = 5 \) and \( x = -2 \), so the correct answer is:

\[
\boxed{2 \text{ and } -5}
\]

Would you like more details or further explanation?

Here are 5 related questions to expand on this concept:
1. How do you find the roots of a quadratic equation using the quadratic formula?
2. What does it mean for a quadratic equation to have no real roots?
3. Can every quadratic equation be factored easily?
4. What is the significance of the discriminant in determining the roots?
5. How can you verify if the roots are correct by substituting them back into the equation?

**Tip**: When factoring quadratics, always check the product and sum of the factors to ensure accuracy!

What are the roots of y = x^2 – 3x – 10?

Discover how to find the roots of the quadratic equation y = x^2 - 3x - 10 using factoring. This detailed guide walks through the step-by-step solution, exploring key algebraic concepts, including the factoring technique for quadratic equations. Ideal for students in Grades 7-9.

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