# How do you use the Rational Root Theorem to find all the roots of #x^3 + 9x^2 + 19x – 4 = 0#?

##### 1 Answer

Aug 23, 2016

The roots are:

#### Explanation:

#f(x) = x^3+9x^2+19x-4#

By the rational roots theorem any *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1, +-2, +-4#

Trying each in turn, we find:

#f(-4) = -64+9(16)+19(-4)-4 = -64+144-76-4 = 0#

So

#x^3+9x^2+19x-4 = (x+4)(x^2+5x-1)#

We can solve the remaining quadratic using the quadratic formula:

#x = (-5+-sqrt(5^2-4(1)(-1)))/(2*1)#

#=(-5+-sqrt(29))/2#