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:

ax^{2}+ bx + c = 0 unknown: x parameters: a, b, c

ax^{2} - (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 3x

^{2}- 12m^{2}= 0, where x is the variable.**Solution**:

3x^{2}- 12m^{2}= 0

3x^{2}= 12m^{2}

x^{2}= 4m^{2}

x =

So we have:

Solve the incomplete literal equation

*my*with^{2}- 2aby = 0,*m0*, being*y*the variable.**Solution***my*^{2}- 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:

*my ^{2} - 2aby = 0*

* my ^{2 }= 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:**x*where x is the variable.^{2}- 2abx - 3a^{2}B^{2},**Solution**:

We have*a = 1, b = -2ab and c = -3a*^{2}B^{2}

Therefore:

Thus we have: V = {- ab, 3ab}.