# Factorization using Quadratic Formula

Factorization using Quadratic Formula: The easiest method to find the roots of quadratic equation is by using Quadratic Formula, Where a, b are coefficients of x^{2}and x respectively and c is a constant term.

**1 ) If b**

(real and equal roots )

2) If b

3) If b

b

^{2}- 4ac = 0 then we have one root only, x = -b/ 2a.(real and equal roots )

2) If b

^{2}- 4ac > 0 then we have two roots one root is having "+" and other involving "-"(real and distinct roots )3) If b

^{2}- 4ac < 0 then no real roots (Complex roots).b

^{2}- 4ac is called the " Discriminant".----------------------------------------------------------------

**Write the discriminant of the following equations.**

1) x

^{2}- 4x + 2 = 0

**Solution :**

x

^{2}- 4x + 2 = 0

Here, a = 1, b = -4 and c = 2

Discriminant = D = b

^{2}- 4ac

= (-4)

^{2}- 4(1)(2)

= 16 - 8

= 8

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2) 3x

^{2}+ 2x - 1 = 0

**Solution :**

3x

^{2}+ 2x - 1 = 0

Here, a = 3, b = 2 and c = -1

Discriminant = D = b

^{2}- 4ac

= (2)

^{2}- 4(3)(-1)

= 4 + 12

= 16

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**Examples on factorization using quadratic formula**

Find the roots using quadratic formula 2 m

^{2}+ 2m – 12 =0

**Solution:**Here, a = 2, b = 2 and c = -12

So plug in these values in the formula, we get

-2 ~+mn~ √[2

^{2}- 4(2)(-12)]

x = --------------------------

2(2)

-2 ~+mn~ √[4 + 96]

x = -----------------------

4

-2 ~+mn~ √ 100

x = -----------------

4

-2 ~+mn~ 10

x = --------

4

- 2 + 10 -2 -10

x = ------ x = ------

4 4

x = 8/4 x = -12/4

x = 2 or x = -3 are the roots of the given equation.

2) Solve : x

^{2}+ 4x + 3 = 0

**Solution:**x

^{2}+ 4x + 3 = 0

a= 1, b = 4 and c =3

Using quadratic formula,

-4 ~+mn~ √[4

^{2}- 4(1)(3)] -4 ~+mn~ √ 4

x = --------------------------= ---------

2(1) 2

-4 + 2 -4 - 2

x = ------ or x = ------

2 2

The roots are { -1,-3}

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**Quadratic Equation Calculator**

Enter the coefficients for the Axwhere ^{2} +
Bx + C = 0 A is the coefficient of x^{2}, B is a coefficient of x and C is a constant term of the equation.Quadratic Equation will output the solutions (give you the root of the equation) (if they are not imaginary).
If A=0, the equation is not quadratic. |

**Introduction of Quadratic Equations**

• Splitting of middle term

• Completing square method

• Factorization using Quadratic Formula

• Solved Problems on Quadratic Equation

• Splitting of middle term

• Completing square method

• Factorization using Quadratic Formula

• Solved Problems on Quadratic Equation