how do you find all real zeros of the polynomial function.
y=4x<cubed>+15x <squared>-8x-3
The function does not have rational roots, as it does not factor.
If you graph the function, you will find approximate values (3 of them) of the real roots.
One of them is positive, and two are negative.
To locate them without graphing, you can find f'(x) and equate to zero to get the location of the extrema.
Since f(-2.74)=49.25 and f(0.243)=-4, we conclude there are indeed 3 real roots, one is < -2.74, one is between -2.74 and .243, and the largest one is > 0.243.
Use either Newton's method or other numerical methods to refine the approximate values of the zeroes.
Ans: -4.185, -0.2584, 0.693 (approx.)