Which are real zeroes of this function?

Algebra
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what are real zeroes of this function?

Sep 3rd, 2015

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How to find the zeros of functions; tutorial with examples and detailed solutions. The zeros of a function f are found by solving the equation f(x) = 0.

Example 1: Find the zero of the linear function f is given by f(x) = -2 x + 4

Solution to Example 1 

To find the zeros of function f, solve the equation 

f(x) = -2x + 4 = 0 

Hence the zero of f is give by 

x = 2

Example 2: Find the zeros of the quadratic function f is given by f(x) = -2 x 2 - 5 x + 7

Solution to Example 2 

Solve f(x) = 0 

f(x) = -2 x 2 - 5 x + 7 = 0 

Factor the expression -2 x 2 - 6 x + 8 

(-2x - 7)(x - 1) = 0 

and solve for x 

x = -7 / 2 and x = 1 

The graph of function f is shown below. The zeros of a function are the x coordinates of the x intercepts of the graph of f. find zeros, example 2

Example 3: Find the zeros of the sine function f is given byf(x) = sin(x) - 1 / 2

Solution to Example 3 

Solve f(x) = 0 

sin (x) - 1 / 2 = 0 

Rewrite as follows 

sin (x) = 1 / 2 

The above equation is a trigonometric equation and has an infinite number of solutions given by 

x = Pi / 6 + 2 k Pi and x = 5 Pi / 6 + 2 k Pi where k is any integer taking the values 0 , 1, -1, 2, -2 ... 

The graph of f is shown below. The number of zeros of function f defined by f(x) = sin(x) - 1 / 2 are is infinite simply because function f is periodic. 

find zeros, example 3Pin it!Share on Facebook

Example 4: Find the zeros of the logarithmic function f is given by f(x) = ln (x - 3) - 2

Solution to Example 4 

Solve f(x) = 0 

ln (x - 3) - 2 = 0 

Rewrite as follows 

ln (x - 3) = 2 

Rewrite the above equation changing it from logarithmic to exponential form 

x - 3 = e 2

and solve to find one zero 

x = 3 + e 2

Example 5: Find the zeros of the exponential function f is given by f(x) = ex2 - 2 - 3


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Sep 3rd, 2015

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