find the quadratic equation given the roots (3, -4)

To find the quadratic equation given the roots \( 3 \) and \( -4 \), we can use the fact that a quadratic equation with roots \( r_1 \) and \( r_2 \) can be written as:

\[
(x - r_1)(x - r_2) = 0
\]

In this case, \( r_1 = 3 \) and \( r_2 = -4 \), so the equation becomes:

\[
(x - 3)(x + 4) = 0
\]

Now, expand the product:

\[
x^2 + 4x - 3x - 12 = 0
\]

Simplifying:

\[
x^2 + x - 12 = 0
\]

Thus, the quadratic equation is:

\[
x^2 + x - 12 = 0
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the quadratic equation change if the roots were \(5\) and \(2\)?
2. What is the general form of a quadratic equation?
3. How do you find the vertex of a quadratic equation?
4. Can you determine the axis of symmetry for \(x^2 + x - 12 = 0\)?
5. What role does the discriminant play in quadratic equations?

**Tip:** You can always check your quadratic equation by substituting the roots back into the equation to verify.

Find the quadratic equation given the roots (3, -4).

Learn how to find a quadratic equation given the roots 3 and -4. This step-by-step guide covers the use of the quadratic equation formula and the Root-Factor Theorem, making it suitable for students in Grades 8-10.

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