Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Translate quadratic graph behavior into root values and multiplicities
Problem
The displayed real-coefficient parabola crosses the \(x\text{-}\text{axis}\) at \(x=2\) and \(x=5\). State \(\text{both}~\text{roots}\) and infer each multiplicity from the crossing behavior.
Graphical roots are the x-coordinates of x-axis intercepts, and crossing behavior carries multiplicity information. We’ll read both x-values, note that the curve passes through rather than turns back, infer odd multiplicity, and use the quadratic degree to determine each count exactly.
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