Question

If the graph of y = a x 2 + b x + c does not intersect the x -axis, then what is true about the roots? Both are real roots. Both are real roots. Both are imaginary roots. Both are imaginary roots. One is a real root, and one is irrational. One is a real root, and one is irrational. One is a real root, and one is rational.

Answer 1

Both roots are imaginary roots.

Step-by-step explanation:

Consider these things:

If we try to solve x²+1 = 0, notice that we aren't able to solve the equation in Real Number system because there are no negative outputs for quadratic function.

Remember that quadratic function has range greater or equal to the max-min value.

x-axis plane represents the solutions of that equation. If a graph intersects x-axis plane then it has a solution.

While a graph that doesn't have any intersects on x-plane, it means that the equation for that graph doesn't have real solutions but imaginary solutions.

As you may notice some of parabola graph has one intersect, two intersects or none. One intersect is one solution to the equation — Two intersects are two solutions of the equation and lastly, no intersects mean that no real solutions and remain only imaginary solution.