SOLUTION: f(x)=x^3+4x^2-5; 1 One zero is given. Find all others

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Question 1000692: f(x)=x^3+4x^2-5; 1
One zero is given. Find all others
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3%2B4x%5E2-5; if x%5B1%5D=1 means x-1 is a factor of f%28x%29=x%5E3%2B4x%5E2-5
so, factor f%28x%29=x%5E3%2B4x%5E2-5
f%28x%29=x%5E3%2B5x%5E2%2B5x-x%5E2-5x-5
f%28x%29=%28x%5E3-x%5E2%29%2B%285x%5E2-5x%29%2B%285x-5%29
f%28x%29=x%5E2%28x-1%29%2B5x%28x-1%29%2B5%28x-1%29

f%28x%29=%28x-1%29%28x%5E2%2B5x%2B5%29=>x-1 is a factor and x=1 is a zero
now use quadratic formula to find other two zeros:
if 0=x%5E2%2B5x%2B5, others zeros are:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+
x+=+%28-5+%2B-+sqrt%28+25-20+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+5+%29%29%2F2+
solutions:
x+=+%28-5+%2B+sqrt%28+5+%29%29%2F2+=>x+=-1.4+
or
x+=+%28-5+-+sqrt%28+5+%29%29%2F2+=>x+=+-3.6

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2B4x%5E2-5%29+