Because it curves back, you find that most values of Y correspond to two different values of X - so there are two solutions. A quadratic equation is an equation in which one variable usually y is in terms of another usually x where the highest power of that other is 2 i. In the graph of a quadratic equation, the plotted points form a parabola.
Otherwise, if the discriminant is positive, there are two distinct real solutions. In the instance of perfect squareshowever, there will be just one number, which is a double root. Could you ever have three solutions to a quadratic equation? Why are there usually two solutions to a quadratic equation?
An imaginary or complex solution to such a question implies that the parabola touches the x axis at a point not within the real x-y plane; to represent complex or imaginary answers, one must introduce a third dimension, and then the location at which the parabola crosses the y-axis will be apparent.
Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution.
This parabola usually intersects the X axis at two different points. Graphically, this is equivalent of the vertex of a parabola just barely touching the x-axis. Those two points are also the two solutions for the quadratic equation.
If the answer is bigger than 0 then the equation has two differentroots. If the discriminant equals zero, we have what is called a "repeated root" and there is exactly one real solution. The infinitely many solutions only happens when A, B, and C are all equal to zero. MERGE exists and is an alternate of.
If the answer is smaller than 0 negative then there are no realroots. Or there can be a pure real solution or there can be a complex solution. How do you know how many solutions a quadratic equation will have?
By definition, a quadratic equation can have at most two solutions. A quadratic equation always has 2 solutions. Would you like to merge this question into it? Otherwise, we can find the number of solutions by examining the discriminantwhich in this case is the quantity B 2 - 4AC.
Merge this question into Split and merge into it SAVE In Math and ArithmeticAlgebraGeometry Generally, when we say a quadratic equation has no solutions, it means that the graph does not cross the x-axis at all.
Two distinct real solutions.Write the left side as a square and simplify the right side if necessary. who gave geometric figures to prove that if the discriminant is negative, a quadratic equation has no solution.: While al-Khwarizmi himself did not accept negative solutions, later Islamic mathematicians that succeeded him accepted negative solutions.
Then there are no real solutions. Graphically, this would mean that on the xy-plane, the quadratic would not intersect the x-axis. The quadratic does have two complex solutions, which can be shown graphically by graphing on a three-dimensional plane.
Writing a Quadratic Equation Given the Solutions Hint: These are sometimes easiest to do if you write UP the page, starting with the solutions at the bottom – where they would be if you had solved the. Quadratic Equations.
An example of a Quadratic Equation: Quadratic Equations make nice curves, like this one: Name.
The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x 2). The "solutions" to the Quadratic Equation are where it is equal to zero.
Free practice questions for Precalculus - Write a Quadratic Equation When Given Its Solutions. Includes full solutions and score reporting.Download