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.
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