Question

The quadratic equation $x^2-2x-\lambda =0,\lambda \ne 0,$

• A. cannot have a real root if $\lambda <-1$
• B. can have a rational root if $\lambda$ is a perfect square
• C. cannot have an integral root if $n^2-1<\lambda <n^2+2n$ where $n=0,1,2,3,.....$
• D. none of these

Answer 1

Answer: (A), (C)

The correct options are
A cannot have a real root if $\lambda <-1$
C cannot have an integral root if $n^2-1<\lambda <n^2+2n$ where $n=0,1,2,3,.....$

$x^2-2x-\lambda =0$
$D=4+4\lambda <0$
Therefore, equation has no real root when $\lambda <-1$.
and cannot have an integral root if $n^2<\lambda +1$.