Which of the following correctly shows the quadratic formula for the given equation? 3x2 - 6x + 8 = 0

GiveN

3x^2 - 6x + 8 = 0

a = 3

b = -6

c = 8

Determine the factors.

Solution:
In order to solve for the roots of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -6, and when multiplied, the answer is -8. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the formula for the quadratic equation.

x = −b ± √(b^2 − 4ac)/2a
x = −(-6) ± √(-6^2 − 4(3)(8))/2(3)
x = 6 ± √(36 − 96)/6
x = 6 ± √(-60)/6

Since the value of b^2 -4ac < 0 , therefore there is no real roots to the given equation. We cannot take the square root of a negative number, since the answer will be an imaginary number or a complex number.

Final answer:

No real roots