Can a quadratic equation have one real solution?

Can a quadratic equation have one real solution?

A quadratic equation has one solution when the discriminant is zero. From an algebra standpoint, this means b2 = 4ac.

How many real solutions does a quadratic equation have?

2 solutions
How To Solve Them? The “solutions” to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph). Just plug in the values of a, b and c, and do the calculations.

Can a quadratic function have one real solution and one complex solution?

A quadratic equation may take complex values for x but the coefficients are always real. This makes both b and c complex, which is not allowed as they have to be real. This is the reason why if quadratic equations have complex roots, they are in pairs and form complex conjugates.

How do you tell if a quadratic has no solution?

A quadratic equation has no solution when the discriminant is negative. From an algebra standpoint, this means b2 < 4ac. Visually, this means the graph of the quadratic (a parabola) will never touch the x axis. Of course, a quadratic that has no real solution will still have complex solutions.

Which equation has only one solution?

quadratic equation
A quadratic equation only has one solution if the discriminant is zero.

Can a quadratic equation have 3 solutions?

Therefore, the roots of the given quadratic equation are 2 and -23. Hence, a quadratic equation cannot have more than two distinct roots.

What causes the quadratic formula to give a single solution?

The discriminant is the expression b2 – 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.

Do all quadratic equations have two solutions?

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.

Can you have one imaginary solution?

A quadratic equation cannot have one imaginary solution because of the discriminant enclosed in a radical. The discriminant, √(b² – 4ac), determines the nature of the roots and it can only be either 2 real roots, 1 real solution or 2 imaginary roots.

Can a function have one imaginary root?

If this value is negative, you can’t actually take the square root, and the answers are not real. Therefore the real numbers are a subset of the complex number system. The fundamental theorem of algebra says that every polynomial function has at least one root in the complex number system.

How do you know if a quadratic equation has two solutions?

Program to find number of solutions in Quadratic Equation

1. if the discriminant is positive , then the quadratic equation has two solutions.
2. if the discriminant is equal , then the quadratic equation has one solution.
3. if the discriminant is negative , then the quadratic equation has no solution.

How do you write a quadratic formula?

A quadratic equation is written as #ax^2+bx+c# in its standard form. And the vertex can be found by using the formula #-b/(2a)#.

What are the steps to solve the quadratic function?

Now we can solve a Quadratic Equation in 5 steps: Step 1 Divide all terms by a (the coefficient of x 2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

What is the standard form of quadratic formula?

By Nucreisha Langdon. The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are coefficiencts and y and x are variables.

What are the types of quadratic equations?

The quadratic equation can be written in three different forms: the standard form, vertex form, and the quadratic form. You can use either form to graph a quadratic equation; the process for graphing each is slightly different.