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Exercises. Quadratic equations.


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
x
1,2
-
b
± √D
2
a

Vieta theorem

For the mentioned quadratic equation

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
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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Attention!!! After press "Next task" you can not return to previous exercise!





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