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How To Form A Quadratic Equation Whose Roots Are Given

This guide is for those who already have complete knowledge of quadratic equations, as well as for 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.

For those who have no knowledge or comprehension of quadratic equations, please drop your mail in the box below. Once we publish a post about it, you’re sure to receive a notification in your mail.

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, which are 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? Let’s just take a look at the problem below.

After this guide, some questions will be dropped to check if you really understand what we’ve been talking about so far.

Steps to solve questions related to changing the root of quadratic equation

  • Subtract both value 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 and that is why we will be using it.
  • Use bracket to fit both values together.
  • Expand them by multiplying the values together.
  • Collect like terms and either subtract or add depending on the sign to finalize your answer.
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Those are the fours ways from which 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 let’s 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’re having 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 will have to multiply the value with each other. We will multiply the first x with everything in the second bracket 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 that now write out the value you get after expanding the bracket. you should have

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

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Practical questions to deal with

  • -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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