# QUADRATIC EQUATION SOLVER AND CALCULATOR

A quadratic equation is usually in the form:

$$ax^2+bx+c$$

Result:

### What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation.

A quadratic equation typically takes the following form:

$$ax^2+bx+c=0$$

In the above, $a$ is the coefficient of $x^2$.

Keep in mind that $a$ cannot be 0 because if a is 0, ax² would not exist, so the equation becomes a linear equation.

For emphasis, $a≠0$

b is the coefficient of x. b can be equal to 0, that is:

$b=0$

However, the quadratic equation will have a complex root if b equals zero.

c is the constant of the quadratic equation. One of the roots of the quadratic equation would be zero if c is equal to 0.

### What are roots of quadratic equations?

The roots of a quadratic equation are the two values of x that are obtained when solving c equations.

The roots of a quadratic equation are the real solution to the quadratic equations.

Because quadratic roots satisfy the equation, they are sometimes referred to as the solution of the quadratic equation.

As you will know in subsequent headings, a quadratic equation may have real and complex roots.

### How do you solve a quadratic equation?

There are three ways to solve a quadratic equation: by factorization, completing the square method, and by formula.

You must obtain two roots when solving quadratic equations, regardless of the method you use.

### What is a real quadratic root?

A real quadratic root is the root of a quadratic equation that is a real number.

A real number includes any positive number, negative number, zero and irrational numbers.

Therefore, a quadratic equation has a quadratic root if its root is a positive number, negative number, or irrational number.

### What is a complex quadratic root?

A quadratic equation has a complex root if the root(s) of the quadratic equation has an imaginary number.

A complex quadratic root is usually in the form:

$$a±ib$$

where a is a real number and ib is an imaginary number.

Generally, a quadratic equation will have a complex root if its discriminant is lesser than zero.

### What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation is the part of the quadratic formula under the square root.

Recalled that the formula for solving a quadratic equation is :

$$x=\frac{-b±\sqrt{b^2-4ac}}{2a}$$

Under the square root is $b2-4ac$. Therefore, it follows that the discriminant. of a quadratic equation is $b2-4ac$.

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