Solving Polynomial Equations with Complex Solutions — Quiz

Question 4 • Algebra 2 with Probability

Consider the equation 3 x cubed plus 14 x squared minus 14 x plus 60 is equal to 0 The real solution is negative 6 What are the nonreal solutions?

Answer

negative 2 i square root of 26 comma 2 i square root of 26

4 minus 2 i square root of 26 comma 4 plus 2 i square root of 26

the fraction with numerator negative 2 plus i square root of 26 and denominator 3 comma the fraction with numerator negative 2 minus i square root of 26 and denominator 3

the fraction with numerator 2 plus i square root of 26 and denominator 3 comma the fraction with numerator 2 minus i square root of 26 and denominator 3

Explanation

Since −6 is a root, divide the cubic by x + 6 to get 3x² − 4x + 10. Using the quadratic formula, the remaining roots are (4 ± √(16 − 120))/6 = (2 ± i√26)/3. These are the nonreal solutions listed in choice D.

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