Question

After being rearranged and simplified, which of the following equations could

be solved using the quadratic formula? Check all that apply.
A. 5x + 4 = 3x^4 - 2
B. -x^2 + 4x + 7 = -x^2 - 9
C. 9x + 3x^2 = 14 + x-1
D. 2x^2 + x^2 + x = 30

Answer 1

Option C and D

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
`ax^2+bx+c=0` with solution
`x=(-b\pm√(b^2-4ac))/(2a)`

A.
`5x+4=3x^4-2`

Simplifying the equation,

`3x^4-2-5x-4=0`

`3x^4-5x-6=0`

It is not a quadratic equation.

B.
`-x^2+4x+7=-x^2-9`

Simplifying the equation,

`-x^2+4x+7+x^2+9=0`

`4x+16=0`

It is not a quadratic equation.

C.
`9x + 3x^2 = 14 + x-1`

Simplifying the equation,

`3x^2+9x-x-14+1=0`

`3x^2+8x-13=0`

It is a quadratic equation where a=3, b=8 and c=-13.

`x=(-8\pm√(8^2-4(3)(-13)))/(2(3))`

`x=(-8\pm√(220))/(6)`

`x=(-8+√(220))/(6),(-8-√(220))/(6)`

`x=1.13,-3.80`

D.
`2x^2+x^2+x=30`

Simplifying the equation,

`3x^2+x-30=0`

It is a quadratic equation where a=3, b=1 and c=-30.

`x=(-1\pm√(1^2-4(3)(-30)))/(2(3))`

`x=(-1\pm√(361))/(6)`

`x=(-1+19)/(6),(-1-19)/(6)`

`x=3,-3.3`

Therefore, option C and D are correct.

Answer 2

C and D

Explanation:

The quadratic formula is

x= (-b±√b²-4ac)/2a

The formula uses the numerical coefficients in the quadratic equation.

The general quadratic equation is ax²+bx+c where a, b and c are the numerical coefficients

So, lets try and see;

A.

`5x+4=3x^4-2\\\\=3x^4-5x-2-4\\=3x^4-5x-6\\a=3,b=-5,c=-6`

But due to the fact that in this equation you have x⁴, the equation is not a quadratic equation thus can not be solved using this formula

B

`-x^2+4x+7=-x^2-9\\\\\\=-x^2+x^2+4x+7+9\\=4x+16`

C

`9x+3x^2=14+x-1\\\\\\=3x^2+9x-x-14+1\\\\=3x^2+8x-13\\\\\\a=3,b=8,c=-13\\`

D.

`2x^2+x^2+x=30\\\\\\=3x^2+x-30\\\\\\a=3,b=1,c=-30`

From the checking above, the equations will be C and D