How can I find the quadric equation when I know the answer?
There is more than one equation that gives a particular answer.
If you mean QUADRATIC equation and you know BOTH roots a and b, the equation can be written
c(x-a)(x-b) = 0
where c is any constant
If you know only one root (say a), b can be anything, and you get an infinite number of possible equations with 'a' as a solution.
the width of a rectangle is 30m^9n^4p^7 and the lenght is 10m^4p^6.what is the area of the rectangle?
To find the quadratic equation when you know the answer, you need to work backwards using the process called factoring or completing the square. By using the given solution, you can determine the roots of the quadratic equation and derive the equation from there.
Let's say the given answer is x = r, where r is a root of the quadratic equation.
1. Start by using the root r to create a binomial factor. For a root r, the binomial factor will be (x - r).
2. If the quadratic equation has two distinct roots, repeat step 1 for the second root using (x - s), where s is the other root.
3. If the quadratic equation has a repeated root, the binomial factor will be (x - r) squared, which is (x - r)(x - r).
4. Multiply the binomial factors together. If you have a repeated root, square the binomial factor. If you have two distinct roots, multiply the two binomial factors.
5. Simplify and expand the equation to get the quadratic equation in standard form, ax^2 + bx + c = 0, where a, b, and c are the coefficients.
Let's consider an example to illustrate this process:
Suppose the given answer is x = 2, and we want to find the quadratic equation.
1. Using the root r = 2, the binomial factor will be (x - 2).
2. Since we only have one root, we don't need to repeat step 1.
3. Multiply the binomial factor: (x - 2) * (x - 2) = x^2 - 4x + 4.
4. Simplify the equation: x^2 - 4x + 4 = 0.
So, the quadratic equation with a root of x = 2 is x^2 - 4x + 4 = 0.
Remember, this process works when you know a root or a solution of the quadratic equation. If you have multiple roots or more information about the quadratic equation, the process may vary slightly.