SOLUTION: What are all the real zeros of g(x)=3x^4-13x^3-10x^2+x-5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What are all the real zeros of g(x)=3x^4-13x^3-10x^2+x-5      Log On


   

Question 922226: What are all the real zeros of g(x)=3x^4-13x^3-10x^2+x-5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29=3x%5E4-13x%5E3-10x%5E2%2Bx-5 .....write -13x%5E3 as -x%5E3-12x%5E3 and
-10x%5E2 as x%5E2%2B4x%5E2-15x%5E2
g%28x%29=3x%5E4-x%5E3%2Bx%5E2-12x%5E3%2B4x%5E2-4x-15x%5E2%2B5x-5 .. group
g%28x%29=%283x%5E4-x%5E3%2Bx%5E2%29-%2812x%5E3-4x%5E2%2B4x%29-%2815x%5E2-5x%2B5+%29+ factor
g%28x%29=x%5E2%283x%5E2-x%2B1%29-4x%283x%5E2-x%2B1%29-5%283x%5E2-x%2B1+%29
g%28x%29=%28x%5E2-4x-5%29%283x%5E2-x%2B1%29
g%28x%29=%28x%5E2-5x%2Bx-5%29%283x%5E2-x%2B1%29
g%28x%29=%28x%2B1%29%28x-5%29%283x%5E2-x%2B1%29
zeros:
%28x%2B1%29%28x-5%29%283x%5E2-x%2B1%29=0
if %28x%2B1%29=0=>x=-1 ---real solution
if %28x-5%29=0=>x=5 ---real solution
3x%5E2-x%2B1=0...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29+
x+=+%281+%2B-+sqrt%28+1-12+%29%29%2F6+

x+=+%281+%2B-+sqrt%28-11%29%29%2F6+

x+=+%281+%2B-+i%2Asqrt%2811%29%29%2F6+
complex solutions: x+=+1%2F6+%2B+i%2Asqrt%2811%29%29%2F6+ or x+=+1%2F6+-+i%2Asqrt%2811%29%29%2F6+