Sum of the roots of a quadratic equation is 5 less than the product of
the roots. If one root is 1 more than the other root, find the product of
the roots?
Answers
Given : Sum of the roots of a quadratic equation is 5 less than the product of the roots.
one root is 1 more than the other root
To Find : the product of the roots
Solution:
one root is 1 more than the other root,
Let say roots are α & α + 1
Sum of roots = α + α + 1 =2α + 1
Product of roots = α( α + 1) =α² + α
Sum of the roots of a quadratic equation is 5 less than the product of
the roots
=> α² + α - 5 = 2α + 1
=> α² - α - 6 = 0
=> α² - 3α + 2α - 6 = 0
=> α(α - 3) + 2(α - 3) = 0
=> (α - 3)(α +2) =0
α = 3 , - 2
Roots are 3 , 4
or - 2 , - 1
Product of roots = α( α + 1)
= 3(3 + 1) = 12 quadratic equation x² - 7x + 12 = 0
or
= -2(-2 + 1) = 2 quadratic equation x² + 3x + 2 = 0
Products of roots = 12 or 2
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