Difference between revisions of "Finding Roots of an Equation"
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| − | In mathematics, the roots of a function are the x-values that make y = 0. For example, the roots of the polynomial <math> y = x^2 - 4 </math> are 2 and -2, since <math> 0 = x^2 - 4 \implies 0 = (x - 2)(x + 2) \implies x = -2, 2</math>. The roots of <math> y = \frac{(2x - 5)(3 - x)}{x(x^2 + 1)} </math> are 3 and 5/2, since only the numerator needs to equal 0 for y to equal 0. The roots of <math> y = \frac{(x^2 - 4)(x-1)}{(x-2)} </math> 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. | + | In mathematics, the roots (also known as zeros) of a function are the x-values that make y = 0. For example, the roots of the polynomial <math> y = x^2 - 4 </math> are 2 and -2, since <math> 0 = x^2 - 4 \implies 0 = (x - 2)(x + 2) \implies x = -2, 2</math>. The roots of <math> y = \frac{(2x - 5)(3 - x)}{x(x^2 + 1)} </math> are 3 and 5/2, since only the numerator needs to equal 0 for y to equal 0. The roots of <math> y = \frac{(x^2 - 4)(x-1)}{(x-2)} </math> 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== | ==Resources== | ||
Revision as of 16:22, 17 September 2021
In mathematics, the roots (also known as zeros) of a function are the x-values that make y = 0. For example, the roots of the polynomial are 2 and -2, since . 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
