# SOLUTION: Find the roots of the polynomial equation x^3 + x^2 -17x +15 = 0

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 Question 420862: Find the roots of the polynomial equation x^3 + x^2 -17x +15 = 0Found 2 solutions by Alan3354, Edwin McCravy:Answer by Alan3354(30993)   (Show Source): You can put this solution on YOUR website!Try the factors of 15, 1, 3 & 5, both + and minus. Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!``` x³ + x² - 17x + 15 = 0 DesCartes' rule of signs: The possibile number of positive solutions is 2 or none because there are two sign changes going left to right. Since the leading coefficient is 1, the feasible rational solutions are ± the divisor of 15. These are: ±1, ±3, ±5, ±15 We begin with trying 1 to see if it is a solution (root). If it is, great! If it isn't we'll try the next one and keep trying them until we find a rational solution or exhaust these and conclude that it has no rational solutions. Trying 1 as a fesible root: 1 |1 1 -17 15 | 1 2 -15 1 2 -15 0 Wow! the first number we tried turned out to be a solution. That doesn't happen very often. Usually we have to try some others that don't give a 0 in the lower right hand corner of the synthetic division array as a remainder. We are lucky. So we have now factored the equation this way: x³ + x² - 17x + 15 = 0 (x - 1)(x² + 2x - 15) = 0 Now we can factor the quadratic expression in the second parentheses: (x - 1)(x + 5)(x - 3) = 0 Now we use the zero factor property: x - 1 = 0; x + 5 = 0; x - 3 = 0 x = 1 x = -5 x = 3 So the roots (solutions) are 1, -5, and 3 Edwin```