Checkpoint: Writing Equations from Solution

Checkpoint: Writing Equations from Solution

Given the roots –i, 4 determine if there are any missing roots. Then write the polynomial equation in standard form.

$\begin{array}{rcl} \begin{matrix} x = - i, & x = i, & x = 4 \end{matrix} \begin{matrix} (x - (- i)) = 0, & (x - i) = 0, & (x - 4) = 0 \end{matrix} \\ (x + i) (x - i) (x - 4) & = & 0 \\ (x^{2} - i + i - i^{2}) (x - 4) & = & 0 \\ (x^{2} - (- 1)) (x - 4) & = & 0 \\ (x^{2} + 1) (x - 4) & = & 0 \\ x^{3} - 4 x^{2} + x - 4 & = & 0 \end{array}$

Note

Q: Based on the number of roots, what degree do you expect the equation to have? Explain.

 A: Third degree because there are three roots 

Q: What is the classification of this equation? 

A: Cubic polynomial with four terms 

Q: Why is there a missing root with the imaginary number i ? 

A: Because imaginary numbers come in conjugate pairs (which is the Conjugate Root Theorem)