Question

Find the value of $k$ such that the quadratic equation $x^2-(k+6)x+2(2k-1)=0$ has sum of the roots as half of their product.

• A. 1
• B. 2
• C. 3
• D. 7

Answer 1

Answer: (D)

7

The given quadratic equation is
$x^2-(k+6)x+2(2k-1)=0$
Here, $a=1,b=-(k+6),c=2(2k-1)$
Sum of the roots $=\frac{-b}{c}=k+6$
Product of the roots $=\frac{c}{a}=2(2k-1)$
According to the given condition :
Sum of the roots $=\frac{1}{2}\times$ Product of the roots
$k+6=\frac{1}{2}\times 2(2k-1)$
$k+6=2k-1$
$\therefore k=7$