Zeros
Add yours
Sorry, we don't have any videos for this topic yet.
Let teachers know you need one by requesting it
Key Questions

The zeros of a function represent the x value(s) that result in the y value being 0.
The zeros of a function represent the xintercept(s) when the function is graphed.
The zeros of a function represent the root(s) of a function.
The zeros of a function represent the solution(s) of a function.

Answer:
Graph the function on a graphing calculator to see what the xcoordinates are where the function intersects the xaxis.
Explanation:
The zeros of a function are found by determining what xvalues will cause the yvalue to be equal to zero. One way to find the zeros is to graph the function on a graphing calculator to see what the xcoordinates are where the function intersects the xaxis.

A zero of a function is an interception between the function itself and the Xaxis.
The possibilities are: no zero (e.g.
#y=x^2+1# ) graph{x^2 +1 [10, 10, 5, 5]}  one zero (e.g.
#y=x# ) graph{x [10, 10, 5, 5]}  two or more zeros (e.g.
#y=x^21# ) graph{x^21 [10, 10, 5, 5]}  infinite zeros (e.g.
#y=sinx# ) graph{sinx [10, 10, 5, 5]}
To find the eventual zeros of a function it is necessary to solve the equation system between the equation of the function and the equation of the Xaxis (
#y=0# ).  no zero (e.g.

Answer:
If algebraic solutions are not usable, try Newton's method or similar to find numeric approximations.
Explanation:
Quintics and other more complicated functions
If
#f(x)# is a well behaved continuous, differentiable function  e.g. a polynomial, then you can find its zeros using Newton's method.Starting with an approximation
#a_0# , iterate using the formula:#a_(i+1) = a_i  f(a_i)/(f'(a_i))# For example, if
#f(x) = x^5+x+3# , then#f'(x) = 5x^4+1# and you would iterate using the formula:#a_(i+1) = a_i  (a_i^5+a_i+3)/(5a_i^4+1)# Putting this into a spreadsheet with
#a_0 = 1# , I got the values:#a_0=1# #a_1 = 1.166666666666667# #a_2 = 1.134701651504899# #a_3 = 1.133002126375077# #a_4 = 1.132997565917805# #a_5 = 1.132997565885065# #a_6 = 1.132997565885065# If
#f(x)# has several Real zeros, then you may find them by choosing different values of#a_0# .Newton's method can also be used to find Complex zeros in a similar way, but you may prefer to use methods like DurandKerner to find all zeros at once.