Question

For the given function, determine consecutive values of x between which each real zero is located...... f(x)=-12x^4 - 7x^3 - 10x^2 + 11x + 16

Answer 1

Polynomials with big terms tend to have their zeros near the origin. Try evaluating the polynomial at 0, 1, 2, 3, -1, -2, -3 and notice whether it is positive or negative as you move from left to right along the x-axis. If it is negative at -2 and positive at -1, for example, that means there must be a zero between -2 and -1.

Also, you can use Descartes' Rule of Signs to analyze the nature of the roots you will have. That may help you narrow your search. For example, if DRoS indicates only 1 positive real root, you don't need to spend any more time checking values of positive x after you've located the 1 root.