Question

Luminaire solves the problem: 26 + 3* – 12x2 = 0, He gets the following roots: x=0, +2, +3. Luminaire counts 5 solutions when he knows there should be 6. What is the 6th root?

A) x = -1
B) x = -2
C) x = 1
D) x = 4

Answer 1

The missing sixth root of the rearranged equation -12x² + 3x = 0, given the roots x=0, x=2, and x=3, is B) x = -2, when using the quadratic formula.

Step-by-step explanation:

The question provides a quadratic equation ax²+bx+c = 0 and states Luminaire found roots for a similarly structured problem. To find the missing sixth root of the equation 26 + 3x - 12x² = 0, we need to use the quadratic formula to solve the quadratic equation:

The quadratic formula is given by:
x = √((-b ± √(b²-4ac))/2a)

In this equation, a, b, and c represent constants. Since 26 is a typo and irrelevant to the structure of the problem, we will ignore it. After correcting the equation to -12x² + 3x = 0, we can solve for x.

Factoring out an x from both terms, we get: x(-12x + 3) = 0, which gives us the roots x = 0 and x = 1/4.

Given the roots x=0, x=2, and x=3, and assuming that all roots provided are correct, the missing root is not x=-1, x=1, or x=4. Since x=0 is a root, the only possible option from the multiple-choice answers for the missing root is B) x = -2.