# What are all the zeroes of #f(x)= x^3 +2x^2 -3x +20 #?

##### 1 Answer

Nov 28, 2015

#### Explanation:

By the rational root theorem, any rational zeros of

So the possible rational roots are the divisors of

#+-1# ,#+-2# ,#+-4# ,#+-5# ,#+-10# ,#+-20#

After a bit of trial and error, find:

#f(-4) = -64+32+12+20 = 0#

so

#x^3+2x^2-3x+20=(x+4)(x^2-2x+5)#

Find the Complex zeros of the remaining quadratic factor using the quadratic formula:

#x = (-b+-sqrt(b^2-4ac))/(2a) = (2+-sqrt(4-20))/2 = (2+-sqrt(-16))/2#

#= (2+-4i)/2 = 1 +-2i#