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 classm

How do you know if a quadratic equation will have one, two, or no solutions? We calculate the discriminant, b^2-4ac. If it's negative, there are no solutions. If it's positive, there are two solutions. If it's zero, there is one solution. How do you find a quadratic equation if you are only given the solution? If we are given solutions a and b, we plug them into (x-a)(x-b)=0 and the required equation is x^2 - (a+b)x + ab = 0 Is it possible to have different quadratic equations with the same solution? Explain. Yes, if they are multiples of each other, they'll have the same solution(s). For example, x^2 and 2x^2 have the same solution. Provide your classmates with one or two solutions with which they must create a quadratic equation. Solution: -3 , -4 Answer: (x-(-3))(x-(-4))=0 (x + 3)(x + 4)=0 x^2 + 7x + 12 = 0