Question

If the graph of a quadratic polynomial $a{x}^2+bx+c$ does not touch or cut the X-axis (as shown above), which of the following statements is correct?

• A. The corresponding quadratic equation $a{x}^2+bx+c=0$ has NO real roots.
• B. The corresponding quadratic equation $a{x}^2+bx+c=0$ has $1$ real root.
• C. The corresponding quadratic equation $a{x}^2+bx+c=0$ has $2$ real roots.
• D. Nothing can be concluded from the graph.

Answer 1

Answer: (A)

The corresponding quadratic equation $a{x}^2+bx+c=0$ has NO real roots.

If graph does not touch or cut the $x-axis$ then it means $D<0$. So no real roots.