Question

# 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

Medium

Solution

Verified by GMS

Correct option is D)

## The given equation is $P(x)=x_{2}−3x+2k$

Comparing with the standard form of quadratic polynomial $ax_{2}+bx+c=0$ we get

$a=1,b=−3,c=2k$

We know that $α=2a−b+D ,β=2a−b−D $, where $D=b_{2}−4ac$

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 $.

Comparing with the standard form of quadratic polynomial $ax_{2}+bx+c=0$ we get

$a=1,b=−3,c=2k$

We know that $α=2a−b+D ,β=2a−b−D $, where $D=b_{2}−4ac$

Then we get,

$α+β=a−b =1−(−3) $

$α.β=ac =12k $

Now, $α+β=α.β$ ...... (Given)

$∴3=2k$

$∴k=23 $

$∴3=2k$

$∴k=23 $

Hence, the answer is $23 $.