How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. Provide your classmate’s with one or two solutions with which they must create a quadratic equation.

It will depend on the value of b^2-4ac, the part under the square root sign, often called D for discriminant

If D > 0 --- 2 real roots
if D=0 ---- 1 real root
if D< 0 --- 2 imaginary or complex roots

x=2 or x=3

It depends on the question given

If you are given -b+-√b-4ac/2a it's called the almighty formula so a question can be given to you in response you will have to use the almighty formula to get a quadratic equation question

To know how many solutions a quadratic equation will have, you can use the discriminant formula. The discriminant (denoted as Δ) is found by calculating b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the standard form ax² + bx + c = 0.

Based on the discriminant value, the following conditions hold:

1. If Δ > 0, then the quadratic equation will have two distinct solutions (real and different).

2. If Δ = 0, then the quadratic equation will have one real solution (real and equal).

3. If Δ < 0, then the quadratic equation will have no real solutions (complex or imaginary).

If you are given the solutions (also called roots) of a quadratic equation, you can find the quadratic equation by using the fact that the roots are the values of x when the equation equals zero.

For example, let's say the solutions are x = 2 and x = -5. To find the quadratic equation, you start by setting up the factors: (x - 2) and (x + 5). This is done by subtracting the solutions from x with the opposite sign.

Next, you multiply the factors to obtain the quadratic equation: (x - 2)(x + 5). Using the distributive property, you get x² + 5x - 2x - 10. Simplifying this expression, you finally arrive at the quadratic equation x² + 3x - 10 = 0.

Yes, it is possible to have different quadratic equations with the same solution. This happens when the two equations have the same roots but different coefficients. For example, both x² - 4x + 4 = 0 and 2x² - 8x + 8 = 0 have x = 2 as their solution. However, the two equations are different because their coefficients are not the same.

To provide your classmates with one or two solutions to create a quadratic equation, you can give them any set of values for x. For instance, let's use x = 3 and x = -2. Your classmates can then plug these solutions into the factored form of a quadratic equation and expand it to get the quadratic equation.