SOLUTION: -x3 + 5x2 - 11x + 55 = 0 Find the roots of the polynomial equation.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: -x3 + 5x2 - 11x + 55 = 0 Find the roots of the polynomial equation.       Log On


   

Question 802709: -x3 + 5x2 - 11x + 55 = 0 Find the roots of the polynomial equation.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

-x%5E3+%2B+5x%5E2+-+11x+%2B+55+=+0+.....factor, group first two terms together and second two terms together
-%28x%5E3+-5x%5E2%29+-+%2811x+-+55%29+=+0+....factor out x%5E2 from the first group and 11 from the second group
-x%5E2%28x-5%29+-+11%28x+-5%29+=+0+
%28x-5%29+-%28x%5E2%2B11+%29+=+0+....use zero product rule to find roots
if %28x-5%29++=+0+=> x=5.....one real root
if ++-%28x%5E2%2B11+%29+=+0+ => x%5E2=-11=> x=sqrt%28-11%29=>x=i%2Asqrt%2811%29 or x=-i%2Asqrt%2811%29
so, you have one real root x=5, and two complex roots x=i%2Asqrt%2811%29 and x=-i%2Asqrt%2811%29
+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+60%2C-x%5E3+%2B+5x%5E2+-+11x+%2B+55%29+