Every real rooted square equation x_{1}, x_{2}, x_{3} and x_{4} can be composed by the formula:

(x -x |

Example:

Compose the square equation whose roots are:

**Solution:****The)**(x - 0) (x - 0) (x + 7) (x - 7) = 0

x^{2}(x^{2}-49) = 0

x^{4}- 49x^{2}= 0**B)**(x + a) (x - a) (x + b) (x - b) = 0

(x^{2}-The^{2}) (x^{2}-B^{2}) = 0

x^{4}- (a^{2}+ b^{2}) x^{2}+ a^{2}B^{2}= 0

## Root properties of the equation

Consider the equation ax^{4} + bx^{2} + c = 0, whose roots are x_{1}, x_{2}, x_{3} and x_{4} and the equation of the 2nd degree ay^{2} + by + c = 0, whose roots are y 'and y ". From each root of the 2nd degree equation, we get two symmetrical roots for the square. So:

From the above, we can establish the following properties:

**1st property:** the sum of the real roots of the equation is zero.

x |

**2nd property: **the sum of the squares of the real roots of the square equation equals -.

**3rd property:** the product of the real and nonzero roots of the equation equals .