SOLUTION: find the real and complex zeros of p(x) = x^3-x^2-4x-6

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the real and complex zeros of p(x) = x^3-x^2-4x-6      Log On


   

Question 1130355: find the real and complex zeros of p(x) = x^3-x^2-4x-6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

p%28x%29+=+x%5E3-x%5E2-4x-6+..........factor
p%28x%29+=+x%5E3%2B2x%5E2-3x%5E2%2B2x-6x-6+
p%28x%29+=+%28x%5E3-3x%5E2%29%2B%282x%5E2-6x%29%2B%282x-6%29+
p%28x%29+=+x%5E2%28x-3%29%2B2x%28x-3%29%2B2%28x-3%29+
p%28x%29+=+%28x+-+3%29+%28x%5E2+%2B+2x+%2B+2%29
zeros:
0+=+%28x+-+3%29+%28x%5E2+%2B+2x+%2B+2%29
if 0+=+%28x+-+3%29+=>highlight%28x=3%29
if 0+=++%28x%5E2+%2B+2x+%2B+2%29...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+
x+=+%28-2+%2B-+sqrt%28+4-8+%29%29%2F2+
x+=+%28-2+%2B-+sqrt%28+-4+%29%29%2F2+
x+=+%28-cross%282%291+%2B-+cross%282%29i%29%2Fcross%282%29+
x+=+%28-1+%2B-+i%29
=>highlight%28x+=+-1+%2B+i%29 or highlight%28x+=+-1+-+i%29