Determination the quadratic equation whose sum and product Of the roots are9 and 14 respectively
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Answer:
As per question,
α+β=−2
3
α×β=−9
α=
β
−9
The quadratic polynomial,
x
2
−(sum of the roots)x + (product of the roots) = 0
x
2
−(−2
3
)x−9=0
x
2
+(2
3
)x−9=0
α+β=−2
3
α+
α
−9
=−2
3
α
α
2
−9
=−2
3
α
2
+2
3
α−9=0
α
2
+3
3
α−
3
α−9=0
(α+3
3
)(α−
3
)=0
α,β=−3
3
,
3
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