the sum if the roots of a quadratic equation is 9 less than the product of its roots. if one root is 3 more than the other , find the product of its roots
pls answer correctly
Answers
Given : Sum of the roots of a quadratic equation is 9 less than the product of the roots.
one root is 3 more than the other root
To Find : the product of the roots
Solution:
one root is 3 more than the other root,
Let say roots are α & α + 3
Sum of roots = α + α + 3 =2α + 3
Product of roots = α( α + 3) =α² + 3α
Sum of the roots of a quadratic equation is 5 less than the product of
the roots
=> α² + 3α - 9 = 2α + 3
=> α² + α - 12 = 0
=> α² -3α +4α - 12 = 0
=> α(α - 3) + 4(α - 3) = 0
=> (α - 3)(α +4) =0
α = 3 , - 4
Roots are 3 , 6
or - 4 , - 1
Product of roots = α( α + 1)
= 3(3 + 3) = 18 quadratic equation x² - 9x + 18 = 0
or
= -4(-4 + 3) = 4 quadratic equation x² + 5x + 4 = 0
Products of roots = 18 or 4
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