Question

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

Answer 1

Answer:

C and D

Step-by-step 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

Answer 2

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 $ax^2+bx+c=0$ with solution $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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.

$x=\frac{-8\pm\sqrt{8^2-4(3)(-13)}}{2(3)}$

$x=\frac{-8\pm\sqrt{220}}{6}$

$x=\frac{-8+\sqrt{220}}{6},\frac{-8-\sqrt{220}}{6}$

$x=1.13,-3.80$

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.

$x=\frac{-1\pm\sqrt{1^2-4(3)(-30)}}{2(3)}$

$x=\frac{-1\pm\sqrt{361}}{6}$

$x=\frac{-1+19}{6},\frac{-1-19}{6}$

$x=3,-3.3$

Therefore, option C and D are correct.