Question

Which of the following is a solution to the quadratic equation below?x²-3x-54-0A. 9B. -57C. 2D. 27

Answer 1

A. 9

Step-by-step explanation

to solve for x we can use the quadratic formula

it says

`\begin{gathered} for \\ ax^2+bc+c=0 \\ the\text{ solution for x is} \\ x=(-b\pm√(b^2-4ac))/(2a) \end{gathered}`

hence

Step 1

a) let

`\begin{gathered} x^2-3x-54=0\Rightarrow ax^2+bx+c=0 \\ so \\ a=1 \\ b=-3 \\ c=-54 \end{gathered}`

b) now, replace in the formula and evaluate

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ x=(-(-3)\pm√((-3)^2-4(1)(-54)))/(2(1)) \\ x=(-(-3)\pm√(9+216))/(2)=(3\pm√(225))/(2) \\ x=(3\pm15)/(2) \end{gathered}`

so

`\begin{gathered} x_1=(3+15)/(2)=9 \\ x_2=(3-15)/(2)=-6 \end{gathered}`

therefore, the answer is

A. 9

I hope this helps you