In Example 6, change the middle three terms to the left of the = sign to −3x³ + 7x² + 7x, given the same root.

Data from Example 6

Solve the equation 2x⁴ − 5x³ + 11x² − 3x − 5 = 0, given that 1 + 2 j is a root. Because 1 + 2j is a root, we know that 1 − 2j is also a root. Using synthetic division twice, we can then reduce the remaining factor to a quadratic function.

The quadratic factor 2x ² − x − 1 factors into (2x + 1) (x − 1). Therefore, the roots of the equation are 1 + 2j, 1 − 2j, 1, and −1/2. As we can see, the calculator display in Fig. 15.3 shows only the real roots.

2 -5 2 + 4j 2 -3+4j 24j 2-1 11 11- 2j -2j 1+2j -1 -3 4 - 2j 1 - 2j 1+2j 0 -5 1+2j 5 0|1 - 2j