solve for the roots of quadratic equation x²-10x+9=0

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

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

For the given equation \(x^2 - 10x + 9 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -10\)
- \(c = 9\)

Let's plug these values into the quadratic formula:

\[
x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(1)(9)}}{2(1)}
\]

Simplifying:

\[
x = \frac{10 \pm \sqrt{100 - 36}}{2}
\]

\[
x = \frac{10 \pm \sqrt{64}}{2}
\]

\[
x = \frac{10 \pm 8}{2}
\]

Now, calculate the two possible values for \(x\):

1. \(x = \frac{10 + 8}{2} = \frac{18}{2} = 9\)
2. \(x = \frac{10 - 8}{2} = \frac{2}{2} = 1\)

So, the roots of the equation are \(x = 9\) and \(x = 1\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you factor the quadratic equation to find the roots?
2. What is the sum of the roots for the equation \(x^2 - 10x + 9 = 0\)?
3. What would happen if the discriminant \(b^2 - 4ac\) was negative?
4. How does the quadratic formula relate to the graph of a parabola?
5. Can the quadratic formula be used for equations with complex roots?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) first to determine the nature of the roots before solving.

Learn how to find the roots of the quadratic equation x^2 - 10x + 9 = 0 using the quadratic formula. This problem covers algebraic concepts such as quadratic equations, roots of equations, and the discriminant theorem. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation