x^4-25x^2+144=0 written in quadratic form

To rewrite the equation \( x^4 - 25x^2 + 144 = 0 \) in quadratic form, we can use substitution.

Let \( u = x^2 \). This transforms the equation as follows:

\[
x^4 = (x^2)^2 = u^2
\]

So, the original equation becomes:

\[
u^2 - 25u + 144 = 0
\]

This is now a quadratic equation in \( u \). Once we solve for \( u \), we can substitute back \( u = x^2 \) to find the values of \( x \).

Would you like help solving this quadratic equation? Let me know!

Here are 5 related questions:
1. How do we solve the quadratic equation \( u^2 - 25u + 144 = 0 \)?
2. What are the steps for substituting back after solving \( u = x^2 \)?
3. How can we factor a quadratic equation if possible?
4. What is the discriminant of a quadratic equation, and how does it help in solving?
5. Can every quartic equation be transformed into a quadratic?

**Tip:** Always check for possible substitutions when working with higher-degree polynomials. This can simplify the equation significantly!

Rewrite the equation x^4 - 25x^2 + 144 = 0 in quadratic form.

Learn how to rewrite and solve the quartic equation x^4 - 25x^2 + 144 = 0 using substitution, transforming it into a quadratic equation. This problem explains polynomial substitution and the quadratic formula, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation