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goldfiish [28.3K]
3 years ago
11

Which of the following is a zero of the equation ?

Mathematics
1 answer:
Murrr4er [49]3 years ago
4 0

Answer:

7/2

Step-by-step explanation:

f(x)=\frac{4x^2-49}{2x+7}

In order to do this you have to recognize that 4 = 2^2\\49 = 7^2

Then you can use the difference of squares formula:

a^2 -b^2=(a+b)(a-b)

In this case a=2x and b = 7 so the numerator is:

f(x)=\frac{4x^2-49}{49}= \frac{(2x+7)(2x-7)}{2x+7}

Notice that we have a 2x+7 up top and bottom of the fraction so these factors cancel out and we're left with:

f(x)=2x-7

Since we're looking for the zero, this means we're looking for the x -intercept.  Any x - intercept will have y = 0 hence why it's often called the "zero".  In this case f(x) is a more formal way of writing y so you can think of f(x)=y.

So if y=0 we have:

0=2x-7\\7=2x\\\frac{7}{2}=x\\

So:

x=\frac{7}{2}


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