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

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

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

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

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

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

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.

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