Finding Roots of an Equation

In mathematics, the roots of a function are the x-values that make y = 0. For example, the roots of the polynomial $y=x^{2}-4$ are 2 and -2, since $0=x^{2}-4\implies 0=(x-2)(x+2)\implies x=-2,2$. The roots of $y={\frac {(2x-5)(3-x)}{x(x^{2}+1)}}$ are 3 and 5/2, since only the numerator needs to equal 0 for y to equal 0. The roots of $y={\frac {(x^{2}-4)(x-1)}{(x-2)}}$ are -2 and 1. Note that 2 is not a root of this function since it makes both the denominator and numerator 0 (not just the numerator), and 0/0 is undefined.

Resources

• Finding Zeros of Polynomials, Lumen Learning
• Finding Roots, Free Math Help
• Zeros of a Function, Cliff's Notes