 A formula to calculate the roots or solutions of a quadratic equation of the form ax2 + bx + c = 0 is known as the Quadratic Formula which is given as,
where, a is coefficient of x2, 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 b2 > 4ac, there are two distinct real roots.
2.    When b2 = 4ac, there is a single real root.
3.    When b2 < 4ac, there is no real roots.

ax2 + bx + c = 0, where a, b and c are constant values and a≠ 0.
Rewriting the given equation as
ax2 + bx = – c
Dividing both sides by the coefficient of x2 i.e. by a we get
Hence the Quadratic Formula is derived.

### Workout Examples

Example 1: Solve x2 – 7x + 12 = 0 by using quadratic formula.

Solution: Here,
x2 – 7x + 12 = 0
Here,
a = 1
b = –7
c = 12

x = 4, 3

Example 2: Solve (p – q)x2 + (p + q)x + 2q = 0 by using quadratic formula.

Solution: Here,
(p – q)x2 + (p + q)x + 2q = 0
Here,
a = (p – q)
b = (p + q)
c = 2q

or,        6x2-18x+12 = 3x2-5x
or,        6x2–18x+12–3x2+5x = 0
or,        3x2–13x+12= 0

Here,
a = 3
b = –13
c = 12