# Literal equations

The 2nd degree equations in the variable x which have some coefficients or some independent terms indicated by other letters are called literal equations.

Letters that appear in a literal equation, excluding the unknown, are called parameters.

Examples:

ax2+ bx + c = 0 unknown: x parameters: a, b, c

ax2 - (2a + 1) x + 5 = 0 unknown: x parameter: a

## Incomplete Literal Equations

Solving incomplete literal equations follows the same process as numerical equations. Take a look at the examples:

• Solve the incomplete literal equation 3x2 - 12m2= 0, where x is the variable.
Solution:
3x2 - 12m2 = 0
3x2 = 12m2
x2 = 4m2

x =
So we have:

• Solve the incomplete literal equation my2- 2aby = 0, with m0, being y the variable.
Solution
my2 - 2aby = 0
y (my - 2ab) = 0
We therefore have two solutions:
y = 0
or
my - 2ab = 0 my = 2ab y =
Like this:

In the solution of the last example, we would have committed a big mistake if we had thus resolved:

my2 - 2aby = 0

my2 = 2aby

my = 2ab

That way we would get only the solution .

The zero of the other solution was "lost" when we divided both terms by y.

This is a good reason to be very careful about cancellations, thus avoiding division by zero, which is absurd.

## Complete literal equations

The complete literal equations can also be solved by Bhaskara's formula. Follow the example:

• Solve the equation: x2 - 2abx - 3a2B2, where x is the variable.
Solution:
We have a = 1, b = -2ab and c = -3a2B2

Therefore:

Thus we have: V = {- ab, 3ab}.
Next: Relations between Coefficients and Roots