4. Which is the standard form of [tex]x^2 - 3 = 2x - 4x^2 + 6[/tex]?

A. [tex]4x^2 + 2x + 6 = 0[/tex]
B. [tex]5x^2 - 2x - 9 = 0[/tex]
C. [tex]-5x^2 + 2x + 3 = 0[/tex]
D. [tex]3x^2 + 3 = 0[/tex]



Answer :

To determine the standard form of the given equation [tex]\( x^2 - 3 = 2x - 4x^2 + 6 \)[/tex], we need to rearrange all terms so that we have a single quadratic expression set equal to zero.

Here is the step-by-step process:

1. Write down the original equation:
[tex]\[ x^2 - 3 = 2x - 4x^2 + 6 \][/tex]

2. Move all terms to the left side to set the equation to zero:
[tex]\[ x^2 - 3 - 2x + 4x^2 - 6 = 0 \][/tex]

3. Combine the like terms on the left side:
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[ x^2 + 4x^2 = 5x^2 \][/tex]
- Combine the linear terms:
[tex]\[ -2x \][/tex]
- Combine the constant terms:
[tex]\[ -3 - 6 = -9 \][/tex]

Putting these together, we get:
[tex]\[ 5x^2 - 2x - 9 = 0 \][/tex]

Thus, the standard form of the equation [tex]\( x^2 - 3 = 2x - 4x^2 + 6 \)[/tex] is:
[tex]\[ \boxed{5x^2 - 2x - 9 = 0} \][/tex]

So, the correct answer is:
[tex]\[ 5x^2 - 2x - 9 = 0 \][/tex]