Multiple choice

The quadratic equation $ax^2+bx+c=0$ will have two roots equal to zero if $b=0$, $c=0$. Also, roots of $cx^2+bx+a=0$ are reciprocal to the roots of $ax^2+bx+c=0$. A straight line $y=mx+c$ will be an asymptote to the curve $y=f(x)$ if $f\left ( x,mx+c \right )=0$ will have two infinite roots. The value of $\lambda $ for which the equation $\lambda^2-4\lambda +3+\left ( \lambda ^2+\lambda -2 \right )x+6x^2-5x^3=0$ will have two roots equal to zero is:

  1. $3$
  2. $-2$
  3. $0$
  4. $1$
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D Correct answer
Explanation

For zero to be a repeated root, both the constant term and the coefficient of x must be zero. The constant term gives lambda = 1 or 3, while the x coefficient is zero only when lambda = 1.

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