Solving incomplete quadratic equations

The roots of an incomplete quadratic equation

1. If the quadratic equation has the form ax² = 0, then it has a single root x = 0.
2. If the quadratic equation has the form ax² + с = 0, then ax² = -с and, therefore,

x² = -

c/a

. The right side of the last equation is a number that is not equal to zero by the condition. Therefore, if the right side is less than zero, then the equation

x² = -

c/a

, this means that the original equation ax² + с = 0 has no roots. If the right side is greater than zero, then the equation

has two roots The roots of an incomplete quadratic equation ax^2+c=0

3. If the quadratic equation has the form ax² + bx = 0, then using the method of factorization, we get The roots of an incomplete quadratic equation ax^2+ич=0

The roots of an incomplete quadratic equation ax^2+ич=0

Thus, the original equation has two roots x₁=0 и x₂ = -

b/a

Examples of solving incomplete quadratic equations.

Example 1.
Solve the quadratic equation x² - 3x = 0.
Solution.
The equation x² - 3x = 0 is an incomplete quadratic equation, so we will solve it by factoring it:
Solving an incomplete quadratic equation x^2 - 3x = 0

Solving an incomplete quadratic equation x^2 - 3x = 0

Answer: 0, 3.

Example 2.
Solve the equation Solving an incomplete quadratic equation (x^2-2x)/4+(x-2)/2=0

Solution.
Let's bring the left side of the equation to a common denominator:

Solving an incomplete quadratic equation (x^2-2x)/4+(x-2)/2=0

Let's multiply both parts of the equation by 4:
Solve an incomplete quadratic equation (x^2-2x)/4+(x-2)/2=0

Answer: -2, 2.