Question

Does the quadratic functiony = 5x2 + 2x + 4have one, two or no real zeros?Utilize the quadratic formula todetermine the answer.[?] real zeros

Answer 1

Any quadratic function can be written like this:

`y=ax^2+bx+c`

And the zeros of this kind of function are given by the quadratic formula:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Depending on the values of a, b and c a quadratic function can have 0, 1 or 2 real zeros. In order to determinate the amount of zeros you need to look at the square root in the quadratic formula. If the term inside the square root is negative then there are no real zeros. If the term is equal to 0 then there's only one zero. Finally if the term inside the square root is positive then the function has two zeros.

Our function is:

`y=5x^2+2x+4`

Which means that:

`\begin{gathered} a=5 \\ b=2 \\ c=4 \end{gathered}`

Now let's take the term inside the square root of the quadratic formula and substitute a,b and c with the values of our function:

`\begin{gathered} b^2-4\cdot a\cdot c=2^2-4\cdot5\cdot4 \\ 4-80=-76 \end{gathered}`

The result is negative. According to what I've stated before this means that this function has no real zeros so the answer is 0.