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

Answer:

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

Explanation:

Given a quadratic function of the form:

$y=ax^2+bx+c$

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

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

Comparing this with the given application:

$\begin{gathered} x=\dfrac{-3\pm\sqrt{3^2-4(1)\times24}}{2(1)} \\ \implies a=1,b=3,\text{ and }c=24 \end{gathered}$

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.