Question

If $\alpha$ and $\beta$ are the zeroes of polynomial $P\left(x\right)=x^2-3x+2k$, and $\alpha +\beta =\alpha .\beta$, then the value of k is ...............

• A. 3
• B. -3
• C. 1
• D. 3/2

Answer 1

Answer: (D)

3/2

The given equation is $P\left(x\right)=x^2-3x+2k$

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

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

We know that $\alpha =\frac{-b+\sqrt{D}}{2a},\beta =\frac{-b-\sqrt{D}}{2a}$, where $D=b^2-4ac$

Then we get,

$\alpha +\beta =\frac{-b}{a}=\frac{-(-3)}{1}$

$\alpha .\beta =\frac{c}{a}=\frac{2k}{1}$

Now, $\alpha +\beta =\alpha .\beta$ ...... (Given)
$\therefore 3=2k$
$\therefore k=\frac{3}{2}$

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