# Materials on quadratic equations, types of roots and examples of problems

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Mathematical Formulas for Quadratic Equations – Quadratic equations are polynomial equations of the second order (to the power of two)2)) in general y = ax2 + b x + c

where a is not equal to 0 and a is the coefficient of x2b is the parameter of x, and c is a constant (it has no variables).

We must understand this quadratic equation because it is not only found in school exam questions,

But there is always a question about the College Test (SBMPTN), so at least we have to understand the basics first.

## Types of roots of quadratic equations

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Quadratic equations have several types of roots depending on the value of D or what characterizes it. where D = b2 – 4ac with the following conditions,

1. d > 0, ax equation2 + bx + c = 0 has two different real roots
2. d = 0, ax equation2 + bx + c = 0 has real double roots
3. D < 0, ax equation2 + bx + c = 0 has imaginary roots

To solve a quadratic equation, we must be able to determine the roots or value of x.

Since it is a quadratic polynomial equation, the value of x or the roots we define has two possibilities.

How? There are at least three methods that can be used, namely by parsing, perfect squares,

Use the ABC formula. For a better understanding, let’s go directly to the example question!

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## Examples of questions and discussion of Quadratic Equation material

1. Solve and determine the type of root in the quadratic equation x2 + 8x + 15 = 0 using a) analysis, b) perfect squares, c) the ABC formula!

Discuss:

1. factoring

X2 + 8x + 15 = 0

(x + 3) (x + 5) = 0

x + 3 = 0 or x + 5 = 0

So x = -3 or x = -5

So HP (settlement set) = {–3, -5}

1. Excellent box

X2 + 8x + 15 = 0

X2 + 8x = -15

X2 + 8x + 16 = -15 + 16

(x + 4)2 = 1

x + 4 = ± 1

X = 1-4 or X = 1 + 4

So X = -3 or X = -5

So HP (settlement set) = {–3, -5}

1. ABC . formula

Previously, we should know the formula of ABC below,

X2 + 8x + 15 = 0

a = 1, b = 8, c = 15

X(1,2) = –

X(1,2) =

X = (-8-2)/2 or X = (-8 + 2)/2

So X = -5 or X = -3

So HP (settlement set) = {–3, -5}

1. Root type of the quadratic equation x2 + 8x + 15 = 0

d = b2 – 4A

= 82 – 4 (1) (15)

= 4

So D > 4, so the equation x . can be terminated2 + 8x + 15 = 0 has two different real roots

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So this is a discussion of quadratic equation material that you can follow along with simple examples of questions that you can use as an analogy when

Dealing with math problems related to quadratic equations, quadratic inequalities, and others.

We hope this article will provide you with useful information, don’t forget to keep visiting formulamathematika.id to update your math formulas every day so that you are better at math.

Happy learning and thank you. 