Question

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