At quadratic equations are relations of equality that can be written as follows:
ax2 + bx + c = 0
With The, B and ç belonging to the set of real numbers and The ≠ 0. Note that the only coefficient that can never be zero is The. Therefore, there is the possibility of B be equal to zero, of ç be equal to zero or of B and ç be equal to zero. In all three of these cases, the equationofseconddegree is called incomplete.
In this article, we'll study techniques that can be used to solve incomplete high school equations in which the coefficient b is null, that is, b = 0.
Bhaskara's formula
THE Bhaskara's formula is one of the techniques that can be used to solve any equationofseconddegree, including incomplete ones. To use it, we must know the four values of a quadratic equation: the coefficients The, B and ç and the discriminant.
The coefficients a, b and c are obvious in the equation, it's the discriminating (∆) is obtained by the following formula:
∆ = b2 – 4·a·c
THE Bhaskara's formula is as follows:
x = – b ± √∆
2nd
To solve a equationofseconddegree, replace the numerical values of the coefficients in the determinant formula, and then replace the same coefficients and the determinant at formulainBhaskara.
For example, to solve the equation:
x2 – 16 = 0
Note that their coefficients are: a = 1, b = 0 and c = – 16. Replacing these values in the formula of discriminating, we have:
∆ = b2 – 4·a·c
∆ = 02 – 4·1·(– 16)
∆ = 4·16
∆ = 64
Now, replacing the values of the coefficients and ∆ in the formulainBhaskara, we have:
x = – b ± √∆
2nd
x = – 0 ± √64
2
x = ± 8
2
x’ = 4
x’’ = – 4
Resolution by reverse operation
when a equationofseconddegree is incomplete because b = 0, there is a practical method to solve them that makes the whole calculation easier. To use it, just pass the coefficientç for the second member (inverting its sign) and calculate the square root in both members of the equation.
This method only works for equationsofseconddegree where b = 0 and a = 1. if The is another real number, just divide the entire equation by that same value, which will make a = 1.
For example, in the equation:
3x2 – 24 = 0
Divide the entire equation by 3 and then solve it normally:
3x2 – 27 = 0
3 3 3
x2 – 9 = 0
x2 = 9
√x2 = √9
x = ± 3
If the value of c is greater than zero, it will be impossible to solve this equation, because putting this value on the second member would make it negative and there are no real roots of negative numbers.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/equacao-incompleta-segundo-grau-com-coeficiente-b-nulo.htm