Question

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Answer 1

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α,β are the zeroes of x2−(k+6)x+2(2k−1)

i.e, α+β=k+6       ( Sum of roots of quadratic )

and αβ=2(2k−1)    ( Product of roots )

According to question, α+β=21αβ

⇒k+6=22(2k−1)=2k−1

⇒k+6=2k−1

⇒k=7

Hence, the answer is 7.

Answer 2

α,β are the zeroes of x2−(k+6)x+2(2k−1)

i.e, α+β=k+6 ( Sum of roots of quadratic )

and αβ=2(2k−1) ( Product of roots )

According to question, α+β=21αβ

⇒k+6=22(2k−1)=2k−1

⇒k+6=2k−1

⇒k=7

Hence, proved

Explanation:

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