Samples Quadratic Equation

The quadratic equation is an expression having an order of degree 2 for variables. First term of this sample quadratic equation is in the order of two and the second term has order of degree 1 and the last term is constant. If any of the term is not present in the quadratic equation means that the term has a value 0.

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Samples of quadratic equation:

Samples of quadratic equation:
General form of quadratic equation is
ax²+bx+c.
As we saw the first degree of first term is 2, the degree of second term is 1 and third term is constant. Here the first two terms are jointly with a,b constants.

Solving a quadratic equation:
The quadratic equation can be solved by using the following formula.
x=`(-b +- sqrt(b^2 -4ac))/(2a)`
There is chance of getting two values as answers. Because of the plus,minus signs.

Example problems for samples of quadratic equation:

Example: 1
Solve the following sample quadratic equation of expression 5x²+2x+1
Solution:

Given quadratic equation is 5x²+2x+1

We know the general quadratic equation is ax²+bx+c.

 Here a=5, b=2 and c=1.

The general formula for solving a quadratic equation is,

x=`(-b +- sqrt(b^2-4ac))/(2a)`

 =`(-2 +- sqrt(2^2 -4.5.1))/(2.5)`

 =`(-2 +- sqrt(4-20))/10`

 =`(-2 +- sqrt (-16))/10`

We can take square root of 16 but it has a negative sign. So we have to consider it as imaginary part and insert i into the square root value.

 =`(-2 +- 4i)/10`

 = `(-1+- 2i)/5`

Answer of the above quadratic equation is `(-1+2i)/5` or `(-1 - 2i)/5`.

Example: 2

Solve the following sample quadratic equation of expression x²+2x+1.

Solution:
Given quadratic equation is

We know the general quadratic equation is ax²+bx+c.

The general formula for solving a quadratic equation is,

                      x=`(-b +- sqrt(b^2 -4ac))/(2a)`
                      = `(-2 +-sqrt(2^2-4.1.1))/(2.1)`
                     = `(-2 +- sqrt(4-4))/2`
                     =`(-2 +- sqrt(0))/2`
                     =`-2/2`

        = -1

Answer for the above quadratic equation is -1.

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Practice problems for samples quadratic equation:

Problem: 1
Solve the following sample quadratic equation of expression2x²+3x+2.
Answer: `(-3 +sqrt(7)i)/6` or `(-3 -sqrt(7)i)/6`

Problem: 2
Solve the following sample quadratic equation of expression 4x²+3x+1
Answer: `(-3 + sqrt(7)i)/8` or `(-3 - sqrt (7)i)/8`.