Factorization using Quadratic Formula

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Enter the coefficients for the Ax2 + Bx + C = 0 where A is the coefficient of x2, 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). Quadratic Equation Ax2 + Bx + C = 0 A = B = C = X1 = X2 = If A=0, the equation is not quadratic.

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 x² and x respectively and c is a constant term.



1 ) If b² - 4ac = 0 then we have one root only, x = -b/ 2a.
(real and equal roots )

2) If b² - 4ac > 0 then we have two roots one root is having "+" and other involving "-"(real and distinct roots )

3) If b² - 4ac < 0 then no real roots (Complex roots).
b² - 4ac is called the " Discriminant".

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Write the discriminant of the following equations.

1) x² - 4x + 2 = 0

Solution :
x² - 4x + 2 = 0

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

Discriminant = D = b² - 4ac

= (-4)² - 4(1)(2)

= 16 - 8

= 8

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2) 3x² + 2x - 1 = 0

Solution :
3x² + 2x - 1 = 0

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

Discriminant = D = b² - 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 m² + 2m – 12 =0

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


So plug in these values in the formula, we get

        -2 ± √[2² - 4(2)(-12)]
x = --------------------------
               2(2)
        -2 ± √[4 + 96]
x = -----------------------
           4
       -2 ± √ 100
x = -----------------
            4
       -2 ± 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 : x² + 4x + 3 = 0

Solution: x² + 4x + 3 = 0

a= 1, b = 4 and c =3

Using quadratic formula,

        -4 ± √[4² - 4(1)(3)]           -4 ± √ 4
x = --------------------------= ---------
              2(1)                                2

     -4 + 2              -4 - 2
x = ------     or x = ------
         2                   2
The roots are { -1,-3}

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Introduction of Quadratic Equations

• Splitting of middle term
• Completing square method
• Factorization using Quadratic Formula
• Solved Problems on Quadratic Equation

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