Question

For what value $k$ , will the equation $x^2-(3k-1)x+2k^2+2k=11$ have equal roots?

• A. $5$
• B. $9$
• C. Both [a] and [b]
• D. $0$

Answer 1

Answer: (C)

Given equation is $x^2-(3k-1)x+2k^2+2k-11=0$
For equal roots $b^2-4ac=0$
$\Rightarrow$ ${(3k-1)}^2=4(2k^2+2k-11)$
$\Rightarrow$ $9k^2+1-6k=8k^2+8k-44$
$\Rightarrow$ $k^2-14k+45=0$
$\Rightarrow$ $(k-5)(k-9)=0$
$\Rightarrow$ $k=5$ or $k=9$