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Class 10

>>Maths

>>Quadratic Equations

>>Standard Form of Quadratic Equations

>>The sum of two roots of a quadratic equa

Question

The sum of two roots of a quadratic equation is 5 and sum their cubes is 35 the equation. Find the equation.

Medium

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Solution

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Let the two roots be α and β

α+β=5 , α

3

+β

3

=35

(α+β)

3

=α

3

+β

3

+3αβ(α+β)

(5)

3

=35+3αβ(5)

125=35+15αβ

90=15αβ

∴

15

90

=αβ

∴αβ=6

Quadratic Eq

n

:

x

2

−(sumofroots)x+productofroots=0

x

2

−(α+β)x+αβ=0

x

2

−5x+6=0