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#