find all complex solutions (real and non-real).

Question

9x³ − 17x² + 88x + 10 = 0

Answer 1

Mel,

1. regroup the terms of the polynomial to factor it

2. Find the values of x that turn each factor zero:

1. 9x³-17x²+88x+10=9x³-18x²+x²+90x-2x+10=9x(x²-2x+10)+

x²-2x+10=(x²-2x+10)(9x+1)=0 Now go to the 2nd step

2. Solve (9x+1)=0 to get 2 real solution

3. Solve the square equation x²-2x+10=0 to get two complex (conjugate) solutions

Good luck

Dr.Ariel

Answer 2

-1/9 is a real root and we can factor out (9x + 1) with synthetic division:

-1/9 | 9 - 17 88. 10

______-1___2__-10____

9 -18 90 0

9x³ - 17x² + 88x + 10 = (9x + 1) (x² - 2x +10)

The reduced quadratic is unfactorable over the reals.