Answer:
Option C and D
Step-by-step explanation:
To find : After being rearranged and simplified, which of the following equations could be solved using the quadratic formula? Check all that apply.
Solution :
Quadratic equation is [tex]ax^2+bx+c=0[/tex] with solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
A. [tex]5x+4=3x^4-2[/tex]
Simplifying the equation,
[tex]3x^4-2-5x-4=0[/tex]
[tex]3x^4-5x-6=0[/tex]
It is not a quadratic equation.
B. [tex]-x^2+4x+7=-x^2-9[/tex]
Simplifying the equation,
[tex]-x^2+4x+7+x^2+9=0[/tex]
[tex]4x+16=0[/tex]
It is not a quadratic equation.
C. [tex]9x + 3x^2 = 14 + x-1[/tex]
Simplifying the equation,
[tex]3x^2+9x-x-14+1=0[/tex]
[tex]3x^2+8x-13=0[/tex]
It is a quadratic equation where a=3, b=8 and c=-13.
[tex]x=\frac{-8\pm\sqrt{8^2-4(3)(-13)}}{2(3)}[/tex]
[tex]x=\frac{-8\pm\sqrt{220}}{6}[/tex]
[tex]x=\frac{-8+\sqrt{220}}{6},\frac{-8-\sqrt{220}}{6}[/tex]
[tex]x=1.13,-3.80[/tex]
D. [tex]2x^2+x^2+x=30[/tex]
Simplifying the equation,
[tex]3x^2+x-30=0[/tex]
It is a quadratic equation where a=3, b=1 and c=-30.
[tex]x=\frac{-1\pm\sqrt{1^2-4(3)(-30)}}{2(3)}[/tex]
[tex]x=\frac{-1\pm\sqrt{361}}{6}[/tex]
[tex]x=\frac{-1+19}{6},\frac{-1-19}{6}[/tex]
[tex]x=3,-3.3[/tex]
Therefore, option C and D are correct.
