How to Solve the Quadratic Equation lm x^2 + (m^2 - lp)x - mp = 0: Step-by-Step Guide

Solving quadratic equations is a fundamental skill in algebra, but sometimes coefficients make them look complicated. This guide will break down the solution process for the equation lm x^2 + (m^2 - lp)x - mp = 0 into easy, manageable steps.

?Watch The Solution

Understanding the Equation

This equation is quadratic because of the x^2 term. We need to solve for x in terms of the other variables: l, m, and p. Using the quadratic formula will allow us to find the solution efficiently.

Step-by-Step Solution

To solve any quadratic equation of the form ax^2 + bx + c = 0, we use the quadratic formula:

x = {-b +- underroot(b^2 – 4ac)}/ 2a

In our equation, we identify:

·?????? a = lm

·?????? b = m^2 - lp

·?????? c = -mp

1.?? Substitute Values into the Formula: Start by plugging these values into the quadratic formula:

?x = \frac{-(m^2 - lp) \pm \sqrt{(m^2 - lp)^2 - 4 \cdot lm \cdot (-mp)}}{2 \cdot lm

2.?? Simplify the Discriminant: Focus on simplifying the discriminant (the part under the square root):

(m^2 - lp)^2 + 4lm *mp

??This expansion will give you a clearer path toward the solution.

3.?? Calculate the Roots: Once the discriminant is simplified, calculate the square root and apply the pm to find the two possible values for \(x\).

?

Practical Applications of Quadratic Equations

Understanding how to solve quadratic equations with complex coefficients is essential in advanced algebra, physics, and engineering. This type of equation frequently appears in real-world scenarios, from calculating projectile motion to optimizing business functions.

?

Conclusion

Solving equations like lm x^2 + (m^2 - lp)x - mp = 0 may seem challenging initially, but using the quadratic formula simplifies the process. By identifying coefficients and simplifying step-by-step, you can find the solution efficiently. With practice, mastering quadratic equations becomes easier, helping you tackle even more complex algebra problems.

?