What method(s) would you choose to solve the equation? Explain your reasoning.
4x^2-48=0
a. Quadratic formula, graphing; the equation cannot be factored easily since the numbers are large.
Selected:b. Square roots; there is no x-term.
c. Factoring; the equation is easily factored.
d. Quadratic formula, completing the square or graphing; the coefficient of x2-term is 1, but the equation cannot be factored.
The correct method to solve the equation 4x^2-48=0 would be to use the quadratic formula, graphing; as mentioned, the equation cannot be factored easily since the numbers are large.
The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / 2a, where the equation is in the form ax^2 + bx + c = 0.
In this case, the equation is 4x^2 - 48 = 0, so a = 4, b = 0, and c = -48. Plugging these values into the quadratic formula, we get x = (0 ± √(0^2 - 4(4)(-48))) / (2(4)).
Simplifying further, x = (± √(0 - (-768))) / 8, which becomes x = ± √(768) / 8.
Hence, x = ± 24/8, which simplifies to x = ±3.
Thus, the solutions to the equation 4x^2 - 48 = 0 are x = 3 and x = -3, which can also be verified by graphing the equation.
To solve the equation 4x^2 - 48 = 0, you have several options. Let's go through each option and reason about which method would be the most appropriate.
a. Quadratic formula, graphing; the equation cannot be factored easily since the numbers are large.
The quadratic formula can be used to solve any quadratic equation, regardless of whether the equation can be factored easily or not. Additionally, graphing can help visualize the solutions, especially if they are not easily expressible in simple terms.
b. Square roots; there is no x-term. (Selected)
In this equation, there is no x-term, which means the coefficient of x is 0. This simplifies the equation to 4x^2 = 48. To solve for x, you can take the square root of both sides of the equation. Since the square root of 48 is not a perfect square, the solutions will involve radical expressions.
c. Factoring; the equation is easily factored.
In this equation, it is not easy to factor out common terms or use any factoring techniques. Factoring is generally more useful when the equation is in a different form.
d. Quadratic formula, completing the square, or graphing; the coefficient of x^2-term is 1, but the equation cannot be factored.
The quadratic formula is always an option to solve quadratic equations, regardless of whether the equation can be factored or not. Completing the square can also be used to solve quadratic equations, but it might be more laborious if the equation cannot be factored easily. Graphing can be helpful for visualization but might not give precise solutions.
Therefore, in this case, the most appropriate method is b. Square roots, as there is no x-term in the equation, making it easier to solve by taking the square roots of both sides of the equation.
4x^2-48=0
No x term, this is the easiest type, first divide each term by 4 to get
x^2 - 12 = 0
add 12 to both sides
x^2 = 12
take √ of both sides
x = ± √12 = ± 2√3