Solving the Equation u³ – 5u² + 6u = 0: Step-by-Step Guide

If you're studying algebra or preparing for exams, solving polynomial equations like u³ – 5u² + 6u = 0 is a fundamental skill. This widely used cubic equation appears in various fields, including physics, engineering, and economics. In this article, we’ll walk through how to factor, solve, and interpret the roots of this equation using clear, beginner-friendly steps.

Understanding the Context

What is the Equation?

The equation to solve is:

u³ – 5u² + 6u = 0

At first glance, this cubic polynomial may seem complex, but it can be simplified using algebraic techniques.

Key Insights

Step 1: Factor Out the Common Term

Notice that each term on the left-hand side contains a u. Factoring out u gives:

u(u² – 5u + 6) = 0

This is the first key step — extracting the greatest common factor.

🔗 Related Articles You Might Like:

📰 Revolutionize Your Bathsuite: The Ultimate Single Sink Vanity You Need! 📰 This Single Sink Bathroom Vanity Is Sustainable, Stylish, and Game-Changing! 📰 Transform Your Bath into Beauty – Discover the Perfect Single Sink Vanity! 📰 The Area Is 6 Times 12 72 Square Cm 📰 The Area Is 12 Times 24 288 Square Meters 📰 The Area Of A Triangle Is 45 Square Units And Its Base Is 9 Units What Is The Height Of The Triangle 📰 The Area Of The Circle Is Pi Times 52 25Pi Square Cm 📰 The Area Of The Garden Is 📰 The Area Of The Square Is 102 100 Square Cm 📰 The Attention Grabbing Truth About Kelsey Grammers Jaw Dropping Net Worth 📰 The Award Winning Komi Just Stunned Fanscan She Talk In Season 3 Heres What Changed 📰 The Awesome Lantern Minecraft Trick Thatll Blow Your Game Away 📰 The Best Leather Belts For Men Boost Confidence Style In Seconds 📰 The Biggest Big Cats At Home Meet 5 Gigantic Cat Breeds That Scare No One 📰 The Biggest Secret To Luxury Sleep King Size Bed Frame Custom Headboard 📰 The Billionaire Like Net Worth Of Lamelo Ball What Youve Never Seen About His Wealth 📰 The Blinding New Ps5 Is Hereokay So Is It Really Worth The Hype Dont Miss Out 📰 The Bottom Of The Ladder Is 5 Meters From The Wall

Final Thoughts

Step 2: Factor the Quadratic Expression

Now focus on factoring the quadratic: u² – 5u + 6

Look for two numbers that multiply to 6 and add up to –5. These numbers are –2 and –3.

So,
u² – 5u + 6 = (u – 2)(u – 3)

Therefore, the equation becomes:

u(u – 2)(u – 3) = 0

Step 3: Apply the Zero Product Property

The Zero Product Property states that if a product of factors equals zero, at least one factor must be zero.