If α and β are the zeroes of polynomial P(x)=x 2 −3x+2k, and α+β=α.β, then the value of k is ............... A 3 B -3 C 1 D 3/2

 Question

If α and β are the zeroes of polynomial P(x)=x2−3x+2k, and α+β=α.β, then the value of k is ...............

A

3

B

-3

C

1

D

3/2

Medium

Solution

Verified by   GMS

Correct option is D)

The given equation is P(x)=x2−3x+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=2a−b+D​​,β=2a−b−D​​, where D=b2−4ac

Then we get,

α+β=a−b​=1−(−3)​

α.β=ac​=12k​

Now, α+β=α.β ...... (Given)
∴3=2k
∴k=23​

Hence, the answer is 23​.