Question

The straight line $x+y=k+1$ touches the parabola $y=x(1-x)$ if

• A. $k=-1$
• B. $k=0$
• C. $k=1$
• D. $k$ takes any real value

Answer 1

The correct option is B $k=0$

Solving $x+y=k+1\text{and}y=x(1-x)$
$\Rightarrow x^2-2x+k+1=0$
Condition for the line to touch the parabola, this equation must have a single solution,
$\Delta =0\Rightarrow (-2{)}^2-4(1\left)\right(k+1)=0\therefore k=0$