How To Derive Quadratic Equations From Their Roots (Step-By-Step)

How to derive quadratic equation from its roots

If you know how to solve quadratic equation, that is not the end of the thing you should know. Now, do you know how to derive quadratic equations from their given roots? Don’t worry, okay? Because will show you everything today.


In today’s article, we will teach you how to construct or make quadratic equation from it given roots.

I hope you have read our article which explained how you can solve quadratic equation by method? If you haven’t, then please click here to read it.


Table of Contents

  1. Methods for deriving quadratic equation from its given roots
  2. Examples of how to construct quadratic equation from its given roots

The roots of a quadratic equation are the values which you get after the quadratic equation has been correctly solved.

Sometimes the roots of a particular quadratic may be given and you can be asked to find its equation. Whenever you are being asked like that, then there are two methods you can use to solve that. You don’t need to panic since you are here.

Read this also: how to mathematically calculate the cut-off mark so that you should know whether JAMB will admit you or not.

Methods To Derive Quadratic Equations From Their Given Roots

The following are an examples and methods of constructing quadratic equation from its given roots.

Method i:

X-(Root of quadratic)X-(Root of quadratic)=0
In this first method, you would need to write the given roots of quadratic equation in the formula provided above

Note: Roots of quadratic equation are usually two.

That is, X-(first given root) X-(second given roots)=0.

Method ii:

The second method for constructing quadratic equation from its given roots involves the use of formula also. And the formula is:

X²-(sum of given roots)X+(product of given roots)=0

I.e, X²-(first given root+second given roots) X+(first given root×second given roots) =0

Examples Of How To Construct Quadratic Equation From It Given Roots

The following are used as an illustrations of how to derive quadratic equation from its given roots.  Please read them carefully.

Below are the examples of how to derive quadratic equations from their roots:

How to construct quadratic equation from the roots

Example 1: -2/5 and -3/7

Solution

Let us use the first method (X-(Root of quadratic)X-(Root of quadratic)=0)

X-(-2/5)x-(-3/7

X+(2/5)x+(2/5)=0

pairing:

x²+(x+3/7)+2/5(x+3/7)

x²+3x/7+2x/5+6/35

LCM=35, then divide by 35

x²×35/1+3x×35/7+2x×35/5+6×35/35=0

35x²+15x+14x+6=0

35x²+29x+6=0

Example 2: -3 and +6

Solution

Let’s us method ii X²-(sum of given roots) X+(product of given roots)=0

X²-(-3+(+)6)x+(-3×(+6)>=0

X²+(3+6)x+(-18)=0

X²+3x+6x-18=0

X²+9x-18=0

Example 3: √3 and √5

Solution

X-(√3)x-(√5)=0

Pairing and grouping:

X(X-√5)-√3(X-√5)=0

X²-√5X-√3X+√15=0

Example 4: 4 and 3/2

Solution

X²-(4+3/2)x+(4×3/2)=0

X²-(11/2)x+6/1=0

LCM=2, then let divide them by 2

2X²-11x+12=0.

Conclusion

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Read this also: Solutions Of Quadratic Equation With Step-By-Step Examples & Formulae

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