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Rules. Quadratic equation and its solution.

A quadratic equation is a polynomial equation of the second degree. The general form is

a x
2 +
b x
+
c
= 0,
where
a
≠ 0.

Solve quadratic equation means to find all the values

xi
, in which will be the equality
a xi
2 +
b xi
+
c
= 0.

Necessary to calculate the discriminant for solving the quadratic equation
∆ =
b
2 - 4
a c
.
• If the discriminant is positive (∆ > 0), then there are two distinct roots, both of which are real numbers.
• If the discriminant is zero (∆ = 0), then there is exactly one distinct real root, sometimes called a double root (
x
1 =
x
2).
• If the discriminant is negative (∆ < 0), then there are no real roots.

The roots are given by the quadratic formula
 x1,2 = -b ± √D 2 a

Vieta theorem

x
2 +
px
+
q
= 0
root sum is equal to coefficient
p
which is drawn with the opposite sign and root’s product is equal to free term
q
:
x
1 +
x
2 = -
p
;
x
1
x
2 =
q
.

## Exercise. Solve the quadratic equation:

3
x
2
+
18
x
-
21
= 0

Determine the number of rational roots of the quadratic equation

Please, to find value of rational roots of a quadratic equation, write down the answer and press the button "Submit".

x
1=
x
2=

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