# Effective Way To Solve Mathematical Quadratic Equation (100% Free)

In mathematics lessons, the quadratic equation is an equation of the variable that has the highest power of two. Or some say that this quadratic equation is a polynomial (polynomial) equation which has a second-order (power).

## Ways to Solve Quadratic Equation

So, what are the forms and ways to solve this quadratic equation? Check out the full description below:

Quadratic equations are often referred to as parabolic equations. Because, if the form of a quadratic equation is drawn into the xy coordinate image, it will form a parabolic graph. We can write the quadratic equation in x in its general form as follows: General Form of Quadratic Equation y = ax2 + bx + c

With a, b, c ∈ R and a ≠ 0 Where:

• x is a variable.
• a is the squared coefficient of x2
• b is the liner coefficient of x.
• c is a constant.

The solution or solution to this equation is called the roots of the quadratic equation. Meanwhile, for the meaning of the square itself is the square root of the number x is equal to the number r such that r2 = x, or, in other words, the number r which if we squared (the product of the number itself) will equal x .

From the description above, we can see that the coefficient values ​​a, b, and c determine the parabolic shape of the quadratic equation function in the xy coordinate. The quadratic equation is an equation with the highest power of the variable, namely 2.

The general form of a quadratic equation is written:

ax2 + bx + c = 0, a ≠ 0 and a, b, c elements of R

### Information:

• x is the variable of the quadratic equation
• a is the coefficient of x2
• b is the x coefficient
• c is a constant

## Kinds of Quadratic Equation Roots

To find out the various kinds of roots of a quadratic equation, we can also find out by using the quadratic formula worksheet ua D = b2 – 4ac. If the value of D is formed, we can easily find the various roots. The following are some types of quadratic equations in general, including:

#### Real Root (D ≥ 0):

»Real roots differ if given = D> 0 For example:

Determine the type of root of the equation below:

x2 + 4x + 2 = 0!

From the equation = x2 + 4x + 2 = 0, we can know:

Is known :

a = 1

b = 4

c = 2

##### Settlement:

D = b2 – 4ac

D = 42 – 4 (1) (2)

D = 16 – 8

D = 8 (D> 8, then the root is also the real root but different) »Real root is the same x1 = x2 if you know D = 0

#### As an example:

Prove that the equation below has twin real roots:

2 × 2 + 4x + 2 = 0

From this equation, namely: = 2 × 2 + 4x + 2 = 0, then

Is known:

a = 2

b = 4

c = 2

##### Settlement:

D = b2 – 4ac

D = 42 – 4 (2) (2)

D = 16 – 16

D = 0 (D = 0, as evidenced by real and twin roots)

#### Imaginary Root / Not Real (D <0) For example:

Find the root type of the equation below:

x2 + 2x + 4 = 0!

From this equation, namely: = x2 + 2x + 4 = 0, then. Is known:

a = 1

b = 2

c = 4

##### Settlement:

D = b2 – 4ac

D = 22 – 4 (1) (4)

D = 4 – 16

D = -12 (D <0, so that the roots are not real roots)

#### Rational Root (D = k2)

As an example:

Determine the type of root of the equation below:

x2 + 4x + 3 = 0

From this equation, namely: = x2 + 4x + 3 = 0, then

Is known:

a = 1

b = 4

c = 3

##### Settlement:

D = b2 – 4ac

D = 42 – 4 (1) (3)

D = 16 – 12

D = 4 = 22 = k2 (Because D = k2 = 4, so the root of the equation is a rational root)

## Properties

Properties of the Root of Quadratic Equations and the formula worksheet Quadratic equations also have several types, here are some types and also their properties, see the full review below:

The roots of a quadratic equation are very much determined by the presence of a discriminant value (D = b2 – 4ac) where it distinguishes the types of roots of the quadratic equation into 3, including:

• If D> 0, then the quadratic equation has two different real roots.
• If D is a perfect square, then both roots are rational.
• If D is not a perfect square, then both roots are irrational.
• If D = 0, then the quadratic equation has two common roots (twin roots), real, and also rational.
• If D <O, then the quadratic equation does not have real roots or both roots are not real (imaginary).
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