Mathematics, 07.07.2019 02:30 starreee

Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? quadratic formula: x =

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$x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}$ shows correct substitution of the values a, b, and c from the given quadratic equation -3x^2-2x+6=0 into quadratic formula.

Step-by-step explanation:

Given: The quadratic equation -3x^2-2x+6=0

We have to show the correct substitution of the values a, b, and c from the given quadratic equation -3x^2-2x+6=0 into quadratic formula.

The standard form of quadratic equation is ax^2+bx+c=0 then the solution of quadratic equation using quadratic formula is given as $x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Consider the given quadratic equation -3x^2-2x+6=0

Comparing with general quadratic equation, we have

a = -3 , b = -2 , c = 6

Substitute in quadratic formula, we get,

$x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}$

Simplify, we have,

$x_{1,2}=\frac{2\pm\sqrt{76} }{-6}$

Thus, $x_{1}=\frac{2+\sqrt{76} }{-6}$ and x_{2}=\frac{2-\sqrt{76} }{-6}

Simplify, we get,

$x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}$

Thus, $x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}$ shows correct substitution of the values a, b, and c from the given quadratic equation -3x^2-2x+6=0 into quadratic formula.

Answer from: ShelleyPSeliger

You can use the standard form of quadratic equation to find the correct substitution of the values a, b and c.

The correct substitution of the value a,b and c from the given quadratic equations into the solution form is $x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}$

What is the standard form of quadratic equations?

The standard form of quadratic equations is ax^2 + bx + c = 0

What are the solutions of standard quadratic equation?

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

From given equation 0 = -3x^2 -2x + 6 , we deduce that a = -3, b = -2 and c = 6.

Thus, substituting these values in the solutions' equation:

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\
\\
x = \dfrac{2 \pm \sqrt{4 + 72}}{-6} = \dfrac{2\pm 2\sqrt{19}}{-6} = \dfrac{-1 \mp 2\sqrt{19}}{3}$

Thus, the correct substitution of the value a,b and c from the given quadratic equations into the solution form is $x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}$

Learn more about solutions of quadratic equations here:

link

Answer from: Quest

Ido not know i use to
Which number produces a rational number when added to 0.25?

Answer from: Quest

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

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Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6...

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