Question

The quadratic equation $a{x}^2+bx+c=0$ will have two roots equal to zero if $b=0$, $c=0$. Also, roots of $c{x}^2+bx+a=0$ are reciprocal to the roots of $a{x}^2+bx+c=0$.
A straight line $y=mx+c$ will be an asymptote to the curve $y=f\left(x\right)$ if $f(x,mx+c)=0$ will have two infinite roots.

The value of $\lambda$ for which the equation ${\lambda }^2-4\lambda +3+({\lambda }^2+\lambda -2)x+6x^2-5x^3=0$ will have two roots equal to zero is:

• A. $3$
• B. $-2$
• C. $0$
• D. $1$

Answer 1

Answer: (D)

$1$

For two roots equal to zero $b=0,c=0$ (by passage)
${\lambda }^2-4\lambda +3=0,\lambda =1,3$
${\lambda }^2+\lambda -2=0,\lambda =1,2$
So, $\lambda$ should be $1$.
Hence, option 'D' is correct.