The roots of the cubic equation 2x³ + 3x² - 18x - 27 are x = -3, 3, -3/2.
How to find roots of polynomial.
For p(x) = 2x³ + 3x² - 18x - 27 the possible rational roots are +- 1, +-3, +-9, +- 27.
By trying these values, we can find that x = -3 is a root.
p(-3) = 2(-3)³ + 3(-3)² - 18(-3) - 27
= -54 + 27 + 54 -27
= 0
Therefore, x + 3 is a factor.
Division 2x³ + 3x² - 18x - 27 by x + 3 to find the other factor.
(2x³ + 3x² - 18x - 27)/( x + 3)
= 2x² - 3x - 9.
Factor the quadratic 2x² - 3x - 9.
(x - 3)(2x + 3)
x = 3 or -3/2
So, the roots of the original cubic equation 2x³ + 3x² - 18x - 27 are x = -3, 3, -3/2.