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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = x^2 - 4 } are 2 and -2, since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 = x^2 - 4 \implies 0 = (x - 2)(x + 2) \implies x = -2, 2} . The roots of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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