SOLUTION: Find all real zeroes of the polynomial 3x^3-5x^2-8x-2

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Question 980293: Find all real zeroes of the polynomial 3x^3-5x^2-8x-2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E3-5x%5E2-8x-2=0...............factor, write -5x%5E2 as x%5E2-6x%5E2 and -8x as -2x-6x
3x%5E3%2Bx%5E2-6x%5E2-2x-6x-2=0.....group
%283x%5E3%2Bx%5E2%29-%286x%5E2%2B2x%29-%286x%2B2%29=0
x%5E2%283x%2B1%29-2x%283x%2B1%29-2%283x%2B1%29=0
%283x%2B1%29+%28x%5E2-2x-2%29=0
zeros:
%283x%2B1%29+=0=>highlight%28x=-1%2F3%29
+%28x%5E2-2x-2%29=0....use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4%2B8+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+12+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+4%2A3+%29%29%2F2+
x+=+%28cross%282%291+%2B-+cross%282%29sqrt%28+3+%29%29%2Fcross%282%29+
x+=+%281+%2B-+sqrt%28+3+%29%29+
so, other two zeros are: highlight%28x+=+1+%2B+sqrt%28+3+%29%29+ and highlight%28x+=+1+-+sqrt%28+3+%29%29+