Question

For what values of $k$, the equation $x^2-2(1+3k)x+7(3+2k)=0$ has equal roots ?

• A. $1$ and $-\frac{10}{9}$
• B. $2$ and $-\frac{10}{9}$
• C. $3$ and $-\frac{10}{9}$
• D. $4$ and $-\frac{10}{9}$

Answer 1

Answer: (B)

$2$ and $-\frac{10}{9}$

Given equation $x^2-2(1+3k)x+7(3+2k)=0$
For equal roots, $D=0$
$4(1+3k{)}^2-28(3+2k)=0$
$\Rightarrow k=\frac{-8\pm 28}{18}$
$\Rightarrow k=2,-\frac{10}{9}$
Hence, option 'B' is correct .