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 $P (x) = x^{2} - 3 x + 2 k$ , 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 $P (x) = x^{2} - 3 x + 2 k$

Comparing with the standard form of quadratic polynomial $a x^{2} + b x + c = 0$ we get

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

We know that $α = \frac{- b + D}{2 a}, β = \frac{- b - D}{2 a}$ , where $D = b^{2} - 4 a c$

Then we get,

$α + β = \frac{- b}{a} = \frac{- ( - 3 )}{1}$

$α . β = \frac{c}{a} = \frac{2 k}{1}$

Now, $α + β = α . β$ ...... (Given)
$∴ 3 = 2 k$
$∴ k = \frac{3}{2}$

Hence, the answer is $\frac{3}{2}$ .

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