Write the quadratic in the form ax²+bx+c=0 given the following roots. Answer the questions that follow.      1.) 5 and 9

To write the quadratic equation in the form \( ax^2 + bx + c = 0 \) given the roots 5 and 9, we use the fact that if \( p \) and \( q \) are the roots of a quadratic equation, the equation can be written as:

\[
(x - p)(x - q) = 0
\]

For the given roots 5 and 9, we substitute \( p = 5 \) and \( q = 9 \):

\[
(x - 5)(x - 9) = 0
\]

Now, expand the expression:

\[
(x - 5)(x - 9) = x^2 - 9x - 5x + 45
\]

Simplifying this:

\[
x^2 - 14x + 45 = 0
\]

Thus, the quadratic equation is:

\[
x^2 - 14x + 45 = 0
\]

### Do you want more details or have any questions?

Here are five questions based on this information:

1. How do you find the sum and product of the roots from a quadratic equation?
2. What is the significance of the discriminant in determining the nature of the roots?
3. Can you derive the quadratic equation if only the sum and product of the roots are given?
4. What happens to the quadratic equation when the roots are complex?
5. How do you factor a quadratic expression when the roots are fractional?

**Tip**: Always check your final quadratic by plugging in the roots to ensure the equation holds true!

Write the quadratic in the form ax²+bx+c=0 given the following roots. Answer the questions that follow. 1.) 5 and 9

Learn how to write the quadratic equation in the form ax² + bx + c = 0, given the roots 5 and 9. This step-by-step guide covers key algebraic concepts such as factoring and Vieta's theorem. Ideal for students in Grades 8-10.

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