Final answer:
The roots of the equation 4x² - 12 = 0 are x = 3 and x = -3. This is achieved by rearranging the equation and taking the square root of both sides. The roots of the equation 4x² - 12 = 0 are ±√3. Option a is the correct answer.
Step-by-step explanation:
The question asks about finding the roots of the equation 4x² - 12 = 0. To find the roots, we can rearrange the equation into the standard form of a quadratic equation, ax² + bx + c = 0, where a, b, and c are constants. The given equation is already in this form with a = 4, b = 0, and c = -12.
To solve for x, we first isolate x² by dividing both sides of the equation by 4, giving us x² = 3. Taking the square root of both sides gives us two possible solutions for x, which are x = ±3. Therefore, the roots of the equation are x = 3 and x = -3, which corresponds to option C in the given choices.
The roots of the equation 4x² - 12 = 0 can be found by applying the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 4, b = 0, and c = -12.
Substituting these values into the quadratic formula, we get:
x = (-0 ± √(0² - 4(4)(-12))) / (2(4))
Simplifying further, we have:
x = ± √(48) / 8
As √(48) can be simplified to 4√(3), the roots of the equation are:
x = ± √3