Find all the real zeros of the polynomial 3

Question

Find all the real zeros of the polynomial 

P(x)=x⁴-2x³-13x²-10x

If there is more than one zero write them separated by commas. Give EXACT answers. No decimals.
Its real zeros are x= 

Answer 1

Dear Dalia,

 

Here we go:

 

P(x)=x⁴ - 2x³ - 13x² - 10x

 

P(x) obviously = 0 when x = 0, so there is one of the real zeros.  (x = 0)

 

P(x) can be factored into: x(x -5 )(x + 1)(x + 2) from which it is obvious that x = 5, x = -1 and x = -2 are also real zeros of P(x).

 

Dalia, when confronted by a situation like this, oftentimes the best thing you can do is to try to graph the equation.  Here is a splendid website to which you can go to graph functions very easily:

 

http://www.meta-calculator.com/online/

 

This graphing calculator is free of charge and can make your life a whole lot easier.

 

Good luck!