Question

A value of $k$ for which the quadratic equation $x^2-2x(1+3k)+7(2k+3)=0$ has equal roots, is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

Given equation is $x^2-2x(1+3k)+7(2k+3)=0.$
For equal roots, discriminant $=0$
$\therefore$ $4{(1+3k)}^2=4\times 7(2k+3)$
$\Rightarrow$ $1+9k^2+6k=14k+21$
$\Rightarrow$ $9k^2-8k-20=0$
$\Rightarrow$ $(9k+10)(k-2)=0$
$\Rightarrow$ $k=2,\frac{-10}{9}$