##
**Quadratic
Formula**

A formula to calculate the roots or solutions of a
quadratic equation of the form

**is known as the***ax*^{2}+ bx + c = 0**Quadratic Formula**which is given as,^{2}, b is coefficient of x and c is constant term. We use this formula to find the required solutions (roots) of the given quadratic equation.

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Some special conditions:

*1. When b*

^{2}> 4ac, there are two distinct real roots.*2. When b*

^{2}= 4ac, there is a single real root.*3.*

*When b*

^{2}< 4ac, there is no real roots.###
**Derivation
of Quadratic Formula**

Consider the general quadratic equation

ax

^{2}+ bx + c = 0, where a, b and c are constant values and a≠ 0.
Rewriting the given equation as

ax

^{2}+ bx = – c
Dividing both sides by the coefficient of x

^{2}i.e. by a we get
Hence the

**Quadratic Formula**is derived.###
*Workout
Examples*

*Workout Examples*

*Example 1:*

*Solve x*^{2}– 7x + 12 = 0 by using quadratic formula

*.*

*Solution:*

*Here,*

*x*^{2}– 7x + 12 = 0

*Here,*

*a = 1*

*b = –7*

*c = 12*

*Using quadratic formula,*

*∴*

*x = 4, 3*

*Example 2:*

*Solve (p – q)x*^{2}+ (p + q)x + 2q = 0 by using quadratic formula

*.*

*Solution:*

*Here,*

*(p – q)x*^{2}+ (p + q)x + 2q = 0

*Here,*

*a = (p – q)*

*b = (p + q)*

*c = 2q*

*Using quadratic formula,*

*or, 6x*^{2}-18x+12 = 3x^{2}-5x

*or, 6x*^{2}–18x+12–3x^{2}+5x = 0

*or, 3x*^{2}–13x+12= 0

*Here,*

*a = 3*

*b = –13*

*c = 12*

*Using quadratic formula,*

*You can comment your questions or problems regarding the quadratic equations and formula here.*

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