Question

If the roots of the equation $4x^2+5k=(5k+1)x$ differ by unity, then the negative value of $k$ is

• A. $-3$
• B. $-\frac{1}{5}$
• C. $-\frac{3}{5}$
• D. $Noneofthese$

Answer 1

Answer: (B)

$-\frac{1}{5}$

Let the roots of the equation

$4x^2-(5k+1)x+5x=0$ be $\alpha$ and $\alpha +1$

$\therefore \alpha +\alpha +1=\frac{5k+1}{4}\Rightarrow \alpha =\frac{5k-3}{8}$ and $\alpha (\alpha +1)=\frac{5k}{4}$

$\Rightarrow \frac{(5k-3)(5k-3+8)}{8\times 8}=\frac{5k}{4}$

$\Rightarrow (5k-3)(5k+5)=80k$

$\Rightarrow (5k-3)(k+1)=16k$

$\Rightarrow 5k^2-14k-3=0$

$\Rightarrow (k-3)(5k+1)=0$

$\Rightarrow k=3,\frac{-1}{5}$

Hence, negative value of $k$ is $\frac{-1}{5}$