Question

Which equation could be solved using this application of the quadratic formula?A. x ^ 2 + 6x + 24 = 3x B 3x ^ 2 + 3x + 24 = 3 C. x ^ 2 + 3x - 24 = 3 D x ^ 2 + 3x + 24 = 3

Answer 1

`A.\;x^2+6x+24=3x`

Explanation:

Given a quadratic function of the form:

`y=ax^2+bx+c`

In order to solve for x, we use the quadratic formula:

`$$x=(-b\pm√(b^2-4ac) )/(2a)$$`

Comparing this with the given application:

`\begin{gathered} x=(-3\pm√(3^2-4(1)*24))/(2(1)) \\ \implies a=1,b=3,\text{ and }c=24 \end{gathered}`

From the given options, the equation that can be solved with the given formula is:

`x^2+6x+24=3x`

This is because it simplifies to:

`\begin{gathered} x^2+6x-3x+24=0 \\ \implies x^2+3x+24=0 \end{gathered}`

The correct option is A.