Question

PLEASE HELP ASAP!!!! What is the smallest degree a function can have with no real solutions?​

Answer 1

IF the minimum is >0, there are no real solutions. for a 3rd, 5th, or odd degree polynomial, there is always at least one real solution, as it crosses the x axis, since there is no max or min.

Answer 2

A polynomial function of degree 1 or higher can have real or complex solutions, but a quadratic function of degree 2 or higher can have no real solutions if its discriminant is negative.

The discriminant of a quadratic function of the form ax^2 + bx + c is b^2 - 4ac. If the discriminant is negative, then the quadratic function has no real solutions.

Therefore, the smallest degree a function can have with no real solutions is degree 2, which is a quadratic function.

Explanation: