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Question

If α and β are the zeroes of polynomial P(x)=x23x+2k, and α+β=α.β, then the value of k is ...............

A
3
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B
-3
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C
1
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D
3/2
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Solution

The correct option is C 3/2
The given equation is P(x)=x23x+2k

Comparing with the standard form of quadratic polynomial ax2+bx+c=0 we get

a=1,b=3,c=2k

We know that α=b+D2a,β=bD2a, where D=b24ac

Then we get,

α+β=ba=(3)1

α.β=ca=2k1

Now, α+β=α.β ...... (Given)
3=2k
k=32

Hence, the answer is 32.

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