Advanced application to a cubic equation

Hi Everyone,

This is a math problem I received during a math team meet as practice. I spent an hour on it with no luck. Does anyone have any ideas?

The polynomial function f(x) = x^3 + ax^2 + bx + c has the following properties:

1. At least two of its zeros are distinctive

2. The sum of its zeros is twice the product of its zeros

3. The sum of the squares of the zeros is three times the product of its zeros

4. f(1) = 1

Find the numerical value of c

Any solutions?

-ShadowKnight8702

Re: Advanced application to a cubic equation

Hint:

Check this out:

$\displaystyle x^3-2.0329*10^-20 x^2-1.5695*10^-9 x+3.4235*10^-15$

or:

$\displaystyle f(x)=(-0.000038478 + x) (-2.1879*10^-6 + x) (0.000040666 + x)$

Re: Advanced application to a cubic equation

Quote:

Originally Posted by

**MaxJasper** Hint:

Check this out:

$\displaystyle x^3-2.0329*10^-20 x^2-1.5695*10^-9 x+3.4235*10^-15$

or:

$\displaystyle f(x)=(-0.000038478 + x) (-2.1879*10^-6 + x) (0.000040666 + x)$

Is that really a hint? I think that makes it more confusing.