HOW TO WRITE A QUADRATIC EQUATION IF THE ROOTS ARE GIVEN

How to Write a Quadratic Equation if the Roots are Given ?

When two roots of a quadratic equation are given , the formula to form the quadratic equation is given by

x² - (sum of the roots)x + product of the roots = 0 

If  and ᵦ be the two roots of a quadratic equation are given , then the formula to form the quadratic equation is given by

x² - (α + β) x + αβ = 0

Write a Quadratic Equation if the Roots are Given - Examples

Example 1 :

Construct a quadratic equation whose two roots are 7 and -1

Solution :

Roots are α  =  7 and β  =  -1

x² - (α + β) x + αβ = 0

α + β  =  7 + (-1)

  =  7 - 1

  =  6

α β  =  7(-1)

  = -7

x² - 6 x + (-7)  =  0

x² - 6 x -7  =  0

Example 2 :

Construct a quadratic equation whose two roots are 3 and 15

Solution :

Roots are α  =  3 and β  =  15

α + β  =  3 + 15

  =  18

α β  =  3(15)

  = 45

x² - 18 x + (-45)  =  0

x² - 18 x - 45  =  0

Example 3 :

Construct a quadratic equation whose two roots are -10 and -3

Solution :

Roots are α  =  - 10 and β  =  -3

α + β  =  -10 + (-3)

  = -10 - 3

  = -13

α β  =  -10(-3)

  =  30

x² - (-13) x + 30  =  0

x² + 13 x + 30  =  0

Example 4 :

Construct a quadratic equation whose two roots are -21 and -1

Solution : 

The given roots are α  =  -21 and β  =  -1

α + β  =  -21 + (-1)

  = -21 - 1

  = -22

α β  =  -21(-1)

  =  21

x² - (-22) x + 21 = 0

x² + 22 x + 21 = 0

Example 5 :

Construct a quadratic equation whose two roots are -7 and 4

Solution :

The given roots are α  =  -7 and β  =  4

α + β  =  -7 + 4

  = -3

α β  =  -7(4)

  =  -28

x² - (-3) x + (-28)  =  0

x² + 3 x - 28  =  0

Example 6 :

Construct a quadratic equation whose two roots are -5 and 6

Solution :

Here two roots are -5 and 6

α + β  =  -5 + 6

  =  1

α β  =  -5 (6)

  =  -30

x² - (1) x + (-30)  =  0

x² - x - 30  =  0

After having gone through the stuff given above, we hope that the students would have understood how to frame a quadratic equation with given roots.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Integration of tanx

    Mar 18, 24 01:00 PM

    Integration of tanx

    Read More

  2. integration of Sec Cube x

    Mar 18, 24 12:46 PM

    integration of Sec Cube x

    Read More

  3. Solved Problems on Logarithms

    Mar 17, 24 02:10 AM

    Solved Problems on Logarithms

    Read More