- #1
AlephZero said:think there is a typo in the question. Where it says "f(x) = 0", x should be a number, the same as in f(4) = 0 and f(-2) = -6.
You did the right thing setting up two equations in a, b, and c. If the question was printed correctly you would be able to get three equations.
If f(x) = 0 for every value of x, then a = b = c = 0, but that doesn't make any sense when the question says f(-2) = -6.
Solving for a, b, and c is a fundamental step in many mathematical equations and problems. It allows us to find the values of these variables and use them to solve for other unknown quantities or to understand the relationships between them.
The steps involved in solving for a, b, and c may vary depending on the specific problem, but generally, they involve identifying the equation or problem, isolating the variables, and using mathematical operations to find their values. It is important to follow a systematic approach and double-check the calculations to ensure accuracy.
Some common techniques used to solve for a, b, and c include substitution, elimination, and graphing. Substitution involves replacing one variable with an equivalent expression to simplify the equation. Elimination involves canceling out one variable by adding or subtracting equations. Graphing involves plotting the equations and finding the points of intersection.
Sure, let's say we have the equation 2a + 4b = 12. To solve for a, we can first isolate the variable by subtracting 4b from both sides, giving us 2a = 12 - 4b. Then, we can divide both sides by 2 to get a = (12 - 4b)/2. Similarly, to solve for b, we can first isolate the variable by subtracting 2a from both sides, giving us 4b = 12 - 2a. Then, we can divide both sides by 4 to get b = (12 - 2a)/4.
To check if your solution for a, b, and c is correct, you can plug the values back into the original equation and see if it satisfies the equation. For example, if we solved for a and b in the previous example and got a = 3 and b = 1, we can plug these values into the equation 2a + 4b = 12 and see if it equals 12. If it does, then our solution is correct.