Solution of quadratic equation - Examples, Exercises and Solutions

Methods for solving a quadratic function

In this article, we will learn the three most common ways to solve a quadratic function easily and quickly.

  1. Trinomial
  2. Quadratic Formula
  3. Completing the Square

Reminder:

The basic quadratic function equation is:
Y=ax2+bx+cY=ax^2+bx+c

When:
a a   - the coefficient of X2X^2
b b   - the coefficient of XX
cc - the constant term

  • aa must be different from 00
  • bb or cc can be 00
  • a,b,ca,b,c can be negative/positive
  • The quadratic function can also look like this:
    • Y=ax2Y=ax^2
    • Y=ax2+bxY=ax^2+bx
    • Y=ax2+cY=ax^2+c

Practice Solution of quadratic equation

Exercise #1

Solve the following equation:

x2+5x+4=0 x^2+5x+4=0

Video Solution

Step-by-Step Solution

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

 

We substitute into the formula:

 

-5±√(5²-4*1*4) 
          2

 

-5±√(25-16)
         2

 

-5±√9
    2

 

-5±3
   2

 

The symbol ± means that we have to solve this part twice, once with a plus and a second time with a minus,

This is how we later get two results.

 

-5-3 = -8
-8/2 = -4

 

-5+3 = -2
-2/2 = -1

 

And thus we find out that X = -1, -4

Answer

x1=1 x_1=-1 x2=4 x_2=-4

Exercise #2

x2+9=0 x^2+9=0

Solve the equation

Video Solution

Step-by-Step Solution

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

 

We identify that we have:
a=1
b=0
c=9

 

We recall the root formula:

Roots formula | The version

We replace according to the formula:

-0 ± √(0²-4*1*9)

           2

 

We will focus on the part inside the square root (also called delta)

√(0-4*1*9)

√(0-36)

√-36

 

It is not possible to take the square root of a negative number.

And so the question has no solution.

Answer

No solution

Exercise #3

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number


x2+4x5=0 x^2+4x-5=0

What are the components of the equation?

Video Solution

Answer

a=1 a=1 b=4 b=4 c=5 c=-5

Exercise #4

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number


10x2+5+20x=0 10x^2+5+20x=0

What are the components of the equation?

Video Solution

Answer

a=10 a=10 b=20 b=20 c=5 c=5

Exercise #5

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number


56x2+12x=0 5-6x^2+12x=0

What are the components of the equation?

Video Solution

Answer

a=6 a=-6 b=12 b=12 c=5 c=5

Exercise #1

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

Identifies a,b,c

5x2+6x8=0 5x^2+6x-8=0

Video Solution

Answer

a=5 a=5 b=6 b=6 c=8 c=-8

Exercise #2

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number


8x25x+9=0 -8x^2-5x+9=0

What are the components of the equation?

Video Solution

Answer

a=8 a=-8 b=5 b=-5 c=9 c=9

Exercise #3

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number


x22=0 -x^2-2=0

What are the components of the equation?

Video Solution

Answer

a=1 a=-1 b=0 b=0 c=2 c=-2

Exercise #4

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number


x2+7x=0 x^2+7x=0

What are the components of the equation?

Video Solution

Answer

a=1 a=1 b=7 b=7 c=0 c=0

Exercise #5

a = coefficient of x²

b = coefficient of x

c = coefficient of the constant term


What is the value of c c in the function y=x2+25x y=-x^2+25x ?

Video Solution

Answer

c=0 c=0

Exercise #1

Solve the following equation:

x2+9x+8=0 x^2+9x+8=0

Video Solution

Answer

x1=1 x_1=-1 x2=8 x_2=-8

Exercise #2

Solve the following equation:

2x2+22x60=0 -2x^2+22x-60=0

Video Solution

Answer

x1=5 x_1=5 x2=6 x_2=6

Exercise #3

Solve the following equation:

2x210x12=0 2x^2-10x-12=0

Video Solution

Answer

x1=6 x_1=6 x2=1 x_2=-1

Exercise #4

Solve the equation

3x239x90=0 3x^2-39x-90=0

Video Solution

Answer

x1=15 x_1=15 x2=2 x_2=-2

Exercise #5

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number


what is the value of a a in the equation

y=3x10+5x2 y=3x-10+5x^2

Video Solution

Answer

a=5 a=5