**What are the roots of the quadratic equation x2 + 9x - 10 = 0** 

**What are the roots of the quadratic equation x2 + 9x - 10 = 0** 

{10,-1}

{ -10,1}

{10,1}

{-10,-1}

To find the roots of the quadratic equation \(x^2 + 9x - 10 = 0\), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, the coefficients are:
- \(a = 1\)
- \(b = 9\)
- \(c = -10\)

Substituting these values into the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{9^2 - 4(1)(-10)}}{2(1)}
\]
\[
x = \frac{-9 \pm \sqrt{81 + 40}}{2}
\]
\[
x = \frac{-9 \pm \sqrt{121}}{2}
\]
\[
x = \frac{-9 \pm 11}{2}
\]

This gives two solutions:

1. \(x = \frac{-9 + 11}{2} = \frac{2}{2} = 1\)
2. \(x = \frac{-9 - 11}{2} = \frac{-20}{2} = -10\)

So, the roots are \(x = 1\) and \(x = -10\). 

The correct answer is: **\{-10, 1\}**.

Do you want further details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How can you verify the roots of a quadratic equation?
2. What is the discriminant of a quadratic equation, and what does it tell us?
3. Can a quadratic equation have complex roots?
4. How would you factor \(x^2 + 9x - 10 = 0\) without using the quadratic formula?
5. What happens if the discriminant is zero?

**Tip:** Always check the discriminant \(b^2 - 4ac\) to determine whether the quadratic equation has real or complex roots.

What are the roots of the quadratic equation x^2 + 9x - 10 = 0?

Learn how to find the roots of the quadratic equation x^2 + 9x - 10 = 0 with a detailed step-by-step solution using the quadratic formula. This problem covers key algebraic concepts and is ideal for students in Grades 8-10.

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