Final answer:
The roots of the equation f(x) = 2x³ + 5x² - 28x - 15, given that 2x+1 is a factor, are x = -1/2, x = -5, and x = 3.
Step-by-step explanation:
To find the roots of the equation f(x) = 2x³ + 5x² - 28x - 15 given that 2x+1 is a factor, we need to set f(x) equal to zero and solve for x.
By setting f(x) = 0 and factoring out 2x+1, we get (2x+1)(x²+4x-15) = 0.
Therefore, the roots of f(x) are x = -1/2 (from 2x+1 = 0) and x = -5 or x = 3 (from x²+4x-15 = 0).
corrected question:
Given f(x)=2ˣ³+5ˣ²-28x-15 and 2x+1 is a facter of f(x). Find all the roots of f(x)