FRAMING A QUADRATIC EQUATION WITH GIVEN ROOTS
Framing a Quadratic Equation with Given Roots :
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
Example 1 :
Construct a quadratic equation whose two roots are -2 and -3
Solution :
Roots are α = -2 and β = -3
x² - (α + β) x + αβ = 0
|
α + β = -2 + (-3) = - 2 - 3 = -5 |
(α β) = -2(-3) = 6 |
x2 - (-5) x + (6) = 0
x2 + 5 x + 6 = 0
Example 2 :
Construct a quadratic equation whose two roots are 5 and -3.
Solution :
Roots are α = 5 and β = -3
|
α + β = 5 + (-3) = 5 - 3 = 2 |
α β = 5(-3) = -15 |
x² -2 x + (-15) = 0
x² - 2 x - 15 = 0
Example 3 :
Construct a quadratic equation whose two roots are 1 and 3
Solution :
Given roots are α = 1 and β = 3
|
α + β = 1 + 3 = 4 |
α β = 1(3) = 3 |
x² - 4 x + 3 = 0
Example 4 :
Construct a quadratic equation whose two roots are 24 and -3
Solution :
The given roots are α = 24 and β = -3
|
α + β = 24 + (-3) = 24 - 3 = 21 |
α β = 24(-3) = -72 |
x² - 21 x + (-72) = 0
x² - 21 x - 72 = 0
Example 5 :
Construct a quadratic equation whose two roots are -1 and -5
Solution :
The given roots are α = -1 and β = -5
|
α + β = -1 + (-5) = -1 - 5 = -6 |
α β = -1(-5) = 5 |
x² - (-6) x + 5 = 0
x² + 6 x + 5 = 0
Example 6 :
Construct a quadratic equation whose two roots are -7 and 5
Solution :
The given roots are α = -7 and β = 5
|
α + β = -7 + 5 = -2 |
α β = -7(5) = -35 |
x² - (-2) x + (-35) = 0
x² + 2 x - 35 = 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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