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How To Form a Quadratic Equation with Roots & Sample Questions

This guide is for those who already have complete knowledge of quadratic equations and those who still need to learn quadratic equations. We will explain in detail how you can convert the root of the quadratic equation to standard form.

Let’s continue with the main thing we’re here for. How to change the roots of the quadratic equation back to the original equation. I assume we all know that there are always two values to a quadratic equation: x =? Or x =?.

The roots of the quadratic equation are otherwise called the answer. Now, how can we convert the answer back to the main equation? At the end of this guide, some questions will be dropped to check if you understand what we’ve been discussing.

How to Solve the Root of a Quadratic Equation

  • Subtract both values from any alphabet used to represent them. Here, we are going to use x to denote it. You can use anything, but the alphabet mostly used is x, which is why we will use it.
  • Use a bracket to fit both values together.
  • Expand them by multiplying the values together.
  • Collect like terms and subtract or add depending on the sign to finalize your answer.

Those are the four ways the root of the quadratic equation can be converted back to its regular equation.

Let’s take the example below by following the steps.

Question 1: Find the quadratic equation whose roots are 3 or -1.

This is a particularly interesting question. Based on the question above, we are dealing with the root of a quadratic equation. Don’t forget that, please.

The value of our x has been given to be 3 or -1. In other words, x = 3 or x = -1

  • STEP 1: we have x-3 and x-(-1). Before moving to step two, expand the first bracket x-(-1). To do this, all we need to do is multiply by the sign in front of the bracket, but let’s assume you have a number in front as 4(-1) , you will multiply the -1 by 4. That is just simple algebra if you don’t have the knowledge, glance through the tutorial and solve the practical questions given there. After expanding the bracket, we now have x-3 and x+1
  • STEP 2: The rule says we should enclose both with bracket so therefore, we have (x-3) (x+1).
  • STEP 3: To expand the bracket, we must multiply the value with each other. We will multiply the first x with everything in the second bracket, and likewise the remaining -3 with everything in the second bracket.

You should get this


  • multiply by x we have x²
  • x multiply by + 1 we have + x
  • -3 multiply by x we have – 3x
  • -3 multiply by 1 we have -3

It’s as simple as writing out the value you get after expanding the bracket. you should have


Finally, you will arrive at x2-2x-3. Isn’t it?

Root of Quadratic Equation Questions

  • -2 and 7
  • 5 and -9
  • -5 and 4
  • -1 and -1/2
  • 3 and -6

To know if you truly understand all we have been saying since, bring out your pen and book, then solve the questions above and drop the answer in the comment box.

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