Question

Which of the following is a zero of the equation ?

Answer 1

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:

$x=\frac{7}{2}$