Know the Fundamental Theorem of Algebra and connect it to polynomial roots.
Infer the minimum number of nonreal roots from a polynomial graph and its degree
Problem
Use this graph information to infer the minimum number of nonreal roots: \(\text{degree}~4\) graph has \(2~x\text{-}\text{intercepts}\).
Big Picture
What this problem is really about
Use the degree as a budget of root occurrences, but remember that a graph shows distinct real-zero locations rather than every multiplicity. To find a minimum number of nonreal roots, test whether repeated real roots at the visible intercepts could fill the remaining degree slots. A single valid all-real construction establishes that nonreal roots are not forced by the intercept count alone.
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