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Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x2 + 1 into the quadratic formula? Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(0) EndRoot Over 2(3) EndFraction x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(2) EndRoot Over 2(3) EndFraction x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (3)(1) EndRoot Over 2(3) EndFraction x = StartFraction negative 3 plus or minus StartRoot 3 squared minus 4 (negative 2)(0) EndRoot Over 2(negative 2) EndFraction

Respuesta :

First of all, you have to manipulate the equation into the standard

[tex]ax^2+bx+c=0[/tex]

form. You can simplify the 1's on both sides and you have

[tex]3x^2-2x=0[/tex]

This means that your coefficients are

[tex]a=3,\quad b=-2,\quad c=0[/tex]

And since the solving formula is

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Plugging your values yields

[tex]x_{1,2}=\dfrac{-(-2)\pm\sqrt{(-2)^2-4\cdot 3\cdot 0}}{2\cdot 3}[/tex]

Lanuel

The correct substitution of the values a, b, and c into the quadratic formula is  [tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2\; - \;4(3)(0)}}{2(3)}\\[/tex]

Given the following equation:

  • [tex]1 = -2x + 3x^2 + 1[/tex]

To show the correct substitution of the values a, b, and c into the quadratic formula:

What is a quadratic equation?

A quadratic equation is a mathematical expression in which one (1) of its variables is to the degree (power) of 2 and as such has two roots.

In Mathematics, the standard form of a quadratic equation is given by;

[tex]ax^2 +bx+c=0[/tex]

Thus, we would express the given equation in standard quadratic form as follows:

[tex]1 = -2x + 3x^2 + 1\\ \\ 3x^2 + 1-2x-1=0\\ \\ 3x^2-2x=0[/tex]

Where:

  • a = 3
  • b = -2
  • c = 0

For the quadratic formula:

Mathematically, the quadratic formula is given by:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a} [/tex]

Substituting the parameters into the formula, we have;

[tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2\; - \;4(3)(0)}}{2(3)}\\ [/tex]

Read more on quadratic equation here: https://brainly.com/question/1214333

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