Definition, Properties, Quadratic Equation Formulas and Example Problems

Formula.co.id – After previously we discussed about amplitude formula this time we will discuss material about the quadratic equation formula, we will describe it in detail and complete from the meaning of quadratic equations, properties, formulas, and examples of problems from equations square.

Understanding Quadratic Equations

What is a quadratic equation? you already know, Quadratic equation is an equation of the variable having the highest power of two. The general form is a, b = is coefficient, and c = is constant, and also the roots are the values ​​of variable x which also satisfies the equation.

Properties of Quadratic Equations

Quadratic equations also have their own properties, namely:

• The quadratic equation has 2 positive roots are (x₁ > 0 and x₂ > 0).
• Quadratic equations also have 2 negative roots are (x₁ < 0 and x₂ < 0).
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• The quadratic equation has 2 roots with different signs (one of the roots is negative).
• The quadratic equation has equal and opposite sign (x₁ = -x₂).
• The quadratic equation has inverse root (x₁ = 1/x₂).

Formula Quadratic equation

The form of the quadratic equation formula is:

ax² + bx + c = 0

where a, b, and also c are a set of real numbers and a 0

Information :

• a = Coefficient of x²
• b = coefficient of x
• c = constant term

The form of the Decriminant Formula of the Quadratic Equation is:

D = b² – 4 ac

Information :

• D = the discriminant of the quadratic equation
• b = coefficient x
• a = coefficient x²
• c = constant term

Example Quadratic Equation Problem

1. There is a quadratic equation that is x² + 4x – 6 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 1

b = 4

c = 6

asked: D = …?

Answer:

D = b² – 4 ac

D = 4² – 4(1)(-6)

D = 16 + 24

D = 40

So, The determinant of the quadratic equation is = 40

1. There is a quadratic equation that is 2x² + 6x – 12 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 2

b = 6

c = 12

asked: D = …?

Answer:

D = b² – 4 ac

D = 6² – 4(2)(-12)

D = 36 + 96

D = 132

So, The determinant of the quadratic equation is = 132

1. There is a quadratic equation that is x² + 14x – 8 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 1

b = 14

c = 8

asked: D=…?

Answer:

D=b² – 4 ac

D=14² – 4(1)(-8)

D=196 + 32

D=228

So, The determinant of the quadratic equation is =228

1. There is a quadratic equation that is 4x² + 12x – 22 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 4

b = 12

c = 22

asked: D = …?

Answer:

D = b² – 4 ac

D=12² – 4(4)(-22)

D=144 + 352

D=496

So, The determinant of the quadratic equation is =496

5. There is a quadratic equation that is 21x² + 6x – 12 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 21

b = 6

c = 12

asked: D = …?

Answer:

D = b² – 4 ac

D= 6² – 4(21)(-12)

D= 36 + 1008

D= 1.044

So, The determinant of the quadratic equation is =1.044

6. There is a quadratic equation that is 22x² + 32x – 42 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 22

b = 32

c = 42

asked: D = …?

Answer:

D = b² – 4 ac

D=32² – 4(22)(-42)

D=1024 + 3696

D= 4.720

So, The determinant of the quadratic equation is =4.720

7. There is a quadratic equation that is 13x² + 67x – 25 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 13

b = 67

c = 25

asked: D = …?

Answer:

D = b² – 4 ac

D=67² – 4(13)(-25)

D=4489 + 1300

D= 5.789

So, The determinant of the quadratic equation is = 5.789

8. There is a quadratic equation that is 7x² + 17x – 37 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 7

b = 17

c = 37

asked: D = …?

Answer:

D = b² – 4 ac

D=17² – 4(7)(-37)

D= 289 + 1.036

D= 1.325

So, The determinant of the quadratic equation is = 1.325

9. There is a quadratic equation that is x² + 45x – 15 = 0. find and calculate the discriminant of the quadratic equation!

Solution:

Is known :

a = 1

b = 45

c = 15

asked: D = …?

Answer:

D = b² – 4 ac

D=45² – 4(1)(-15)

D= 2025 + 60

D= 2.085

So, The determinant of the quadratic equation is = 2.085

This is a complete discussion on how to calculate the formula for quadratic equations along with examples of questions and their discussion, hopefully useful...

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