Final answer:
To approximate the real zeros of the function, we can use synthetic division and substitute possible rational zeros to find the real zeros. The real zeros of the function f(x)=-5x³+9x²+12x+2 are approximately -1.5 and -0.3.
Step-by-step explanation:
To approximate the real zeros of the function f(x)=-5x³+9x²+12x+2 to the nearest 10th, we can use a graphing calculator or synthetic division method.
By using synthetic division, we can find that the possible rational zeros of the function are -2, -1.5, -1, -0.5, 1, and 2. By substituting these values into the function, we can find which zeros are actually real.
Based on the calculations, the real zeros of the function are approximately -1.5 and -0.3.