Factorization using Quadratic Formula
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).
If A=0, the equation is not quadratic. |
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) 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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Introduction of Quadratic Equations
• Splitting of middle term
• Completing square method
• Factorization using Quadratic Formula
• Solved Problems on Quadratic Equation