Question

I WILL GIVE BRAINLIEST!!!

Find the solutions of the quadratic equation 6x^2-6x-2=0

Choose 1 answer:

(choice A)
A
$\frac{1}{2}±\sqrt\frac{21}{6}i$

(choice B)
B
$-\frac{1}{2}±\sqrt\frac{21}{6}i$

(choice C)
C
$-\frac{1}{2}±\sqrt\frac{21}{6}$

(choice D)
D
$\frac{1}{2}±\sqrt\frac{21}{6}$

Answer 1

Answer:

$\dfrac{1}{2} \pm \dfrac{\sqrt{21}}{6}$

Step-by-step explanation:

$6x^2 - 6x - 2 = 0$

Divide both sides by 2.

$3x^2 - 3x - 1 = 0$

We compare it to the standard form:

$ax^2 + bx + c = 0$

We have a = 3, b = -3, c = -1.

To factor, we need two numbers that multiply to ac and add to b.

ac = 3 * (-1) = -3

-3 = -3 * 1; -3 + 1 = -2

-3 = -1 * 3; -1 + 3 = 2

There are no two integers whose product is -3 and whose sum is -3, so we cannot factor the trinomial. We use the quadratic formula to solve the equation.

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

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

$x = \dfrac{3 \pm \sqrt{9 + 12}}{6}$

$x = \dfrac{3 \pm \sqrt{21}}{6}$

$x = \dfrac{1}{2} \pm \dfrac{\sqrt{21}}{6}$