Question

If $a>0$ and $b^2-4ac=0$, then the curve $y=a{x}^2+bx+c$

• A. Cuts the x-axis
• B. Touches the x-axis and lies below it
• C. Lies entirely above the x-axis
• D. Touches the x-axis and lies above it

Answer 1

The correct option is D Touches the x-axis and lies above it

The discriminant of quadratic equation $a{x}^2+bx+c=0$ is $b^2-4ac$

which is given zero in the question, so both roots will be equal and real i.e.

the parabola will touch $x-$axis and since $a>0$ so parabola will be upward.

Hence given parabola will touch the x-axis and lies above it.