# Complex Numbers And Quadratic Equations

A complex number is the number which consists of a real number with imaginary number i. x + y. i is the form of imaginary number. Also we know that the square of the real number is either 0 or positive. Complex numbers and quadratic equations have the possible result of the problem, complex numbers are helpful in solving the problem of quadratic equation and also we can solve polynomial equations with the help of the complex numbers. A quadratic equation is the polynomial equation of the second degree. It is written in form of ax2 + bx + c  = 0: where ‘x’ represent the variable and a, b, c are constant with a≠0, if a=0 then the equation will no more be a quadratic equation, then it will be a linear equation. The constant a, b, c are known as the quadratic coefficient, the linear coefficient and the constant term respectively. There are some formulas to calculate the quadratic equation such as completing the square, graphing method, Newton’s method and by using the quadratic formula.

A quadratic equation when computed gives two results which are real and in complex form known as roots. Suppose if we have ax2 + bx + c = 0: then its roots will be estimated by the quadratic formula:

- b ± √ (b– 4ac)

X = _______________,

2a

Here the symbol ± indicates both roots that the result may be in the form of

- b + √ (b– 4ac)

X = _______________          or

2a

- b - √ (b– 4ac)

X = _______________

2a

Now we will understand this with the help of quadratic equation suppose have an equation 2x2 + 6x + 3 = 0.

Now we will substitute the fair values of a, b, c in the quadratic equation i.e. 2, 6, 3 respectively.

- 6 ± √ (6– 4*3*2),

X = _______________

2*2

- 6 ± √ (36– 24)

X = _______________

4

- 6 ± √ (12)

X = ____________,

4

- 6 ± √ 12

X = ________,

4

-  6± 3.4

X = ______,

4

First we will take the root for positive sign

-  6+ 3.4

X = ______   = .65

4

And now we will take the negative sign

-  6- 3.4

X = ______   = 2.35

4

Therefore the outcome of quadratic equation is;

2x2 + 6x + 3 = 0 is .65 and 2.35.

Math Topics