Write a quadratic equation having the given solutions
How do you write the answer to a quadratic equation?
To solve a quadratic equation by factoring,Put all terms on one side of the equal sign, leaving zero on the other side.Factor.Set each factor equal to zero.Solve each of these equations.Check by inserting your answer in the original equation.
What is a quadratic equation with 2 solutions?
It is called the Discriminant, because it can “discriminate” between the possible types of answer: when b2 − 4ac is positive, we get two Real solutions. when it is zero we get just ONE real solution (both answers are the same) when it is negative we get a pair of Complex solutions.
Can a quadratic equation have one solution?
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.
What are 5 methods of solving a quadratic equation?
We have factoring, square root property, completing the square, and the quadratic formula.
What is quadratic equation used for?
As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains.
What equation has two solutions?
Why are there two solutions in quadratic equations?
A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.
How do you know if a quadratic equation has no solution?
If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.
Can a quadratic equation have 3 solutions?
Therefore, our assumption that a quadratic equation has three distinct real roots is wrong. Hence, every quadratic equation cannot have more than 2 roots. Note: If a condition in the form of a quadratic equation is satisfied by more than two values of the unknown then the condition represents an identity.
Which of the equations has only one solution?
An independent system has exactly one solution pair (x,y) . The point where the two lines intersect is the only solution. An inconsistent system has no solution.
Can both the roots of quadratic equation be zero?
Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.