Question

Least number of real zeroes a cubic polynomial can have

Answer 1

Answer:

1

Step-by-step explanation:

Assuming that we're talking about a cubic polynomial with real coefficients, there must be at least one zero.  This is because a cubic tends to ∞ on the right and -∞ on the left, or -∞ on the right and ∞ on the left.  Either way, by the Intermediate Value Theorem, there is a point where it crosses the x-axis, or in other words, there is some zero.

However, there might not be more than 1.  For instance, the simplest cubic

f(x) = x³

only has 1 zero, namely x = 0.

Answer 2

Least number of real zeroes a cubic polynomial can have is 1