Question

Which of the following is a zero of the equation ?

f(x) = 4x^2 -49 / 2x + 7

A. -7/2
B. 7/2
C. 0

And explain why !!! Please

Answer 1

7/2

Explanation:

`f(x)=(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)=(4x^2-49)/(49)= ((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\\(7)/(2)=x\\`

So:

`x=(7)/(2)`