Enter the equation for a quadratic polynomial which has a double root at -7

A quadratic polynomial with a double root at \( x = -7 \) can be written as:

\[
f(x) = a(x + 7)^2
\]

where \( a \) is any non-zero constant. If \( a = 1 \), the equation simplifies to:

\[
f(x) = (x + 7)^2 = x^2 + 14x + 49
\]

This is the quadratic polynomial with a double root at \( x = -7 \).

Would you like further details, or do you have any questions?

Here are 5 related questions you might find helpful:
1. How do you find the roots of a quadratic equation?
2. What does it mean when a quadratic has a "double root"?
3. How can you determine if a quadratic equation has double roots by using its discriminant?
4. Can a quadratic polynomial have two distinct roots? If so, how is it written?
5. How does the value of \( a \) affect the graph of the quadratic polynomial?

**Tip:** A double root occurs when the discriminant of the quadratic equation is zero, which means the graph touches the x-axis at one point but doesn't cross it.

Discover how to write a quadratic polynomial with a double root at x = -7. This solution covers key algebraic concepts, including the double root condition, and provides both factored and expanded forms of the quadratic equation. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation