Question

The values of $k$ for which the roots of the equation $k{x}^2+kx+1=-4x^2-x$ are $k=5,-3$ are real and equal.

• A. True
• B. False

Answer 1

The correct option is B False

$\begin{array}{cc}k{x}^2+kx+1& =-4x^2-x\\ k{x}^2+kx+1+4x^2+x& =0\\ (k+4)x^2+(k+1)x+1& =0\end{array}$

$\Rightarrow$ Compare the given quadratic equation $(k+4)x^2+(k+1)x+1=0$ with, $a{x}^2+bx+c=0$.

$\therefore$ $a=k+4,b=k+1,c=1$

$\Rightarrow$ It is given that roots are real and equal.

$\therefore$ $b^2-4ac=0$

$\begin{array}{cc}(k+1{)}^2-4(k+4)\left(1\right)& =0\\ k^2+2k+1-4k-4& =0\\ k^2-2k-3& =0\\ k^2-3k+k-3& =0\\ k(k-3)+1(k-3)& =0\\ (k-3)(k+1)& =0\\ k-3=0\text{and}k+1& =0\\ k=3\text{and}k& =-1\end{array}$

$\Rightarrow$ Hence, we can see that, given values of $k$ are incorrect.

$\therefore$ Given statement is false.