At quadratic equations are those that have only one unknown, and one of its terms is squared. So, all equationofseconddegree can be written as follows:
ax2 + bx + c = 0
In this form, a, b and c are real numbers, with a ≠ 0. Note that only coefficient a must be non-zero. When one (or all) of the other coefficients of a equationofseconddegree are equal to zero, this equation is called incomplete.
In this article, we'll look at the methods you can use to solve equationsincomplete, in which case the coefficient C = 0, that is, the coefficient is null.
Bhaskara's formula
The best known method, and one that can be used to solve any equationofseconddegree, as long as this equation has real roots, it is the Bhaskara's formula. To use this method, simply substitute the numerical values of the equation's coefficients into the formula for discriminating and then substitute the coefficients and the discriminant in Bhaskara's formula. The formulas cited are as follows:
discriminating:
∆ = b2 – 4·a·c
Bhaskara:
x = – b ± √∆
2nd
Example: a equationincomplete 2x2 + 32x = 0 has how discriminating:
∆ = b2 – 4·a·c
∆ = 322 – 4·2·0
∆ = 322
At formulainBhaskara, the x values will be:
x = – b ± √∆
2nd
x = – 32 ± √322
2·2
x = – 32 ± √322
4
x = – 32 ± 32
4
x’ = – 32 + 32 = 0 = 0
4 4
x’’ = – 32 – 32 = – 64 = 0
4 4
x’’ = – 16
S = {0, – 16}
Putting factors into evidence
In the equations where C = 0, note that in all terms the unknown x appears. In this case, it is possible to put x - and other factors, if any - in evidence and analyze the result of this to find the rootsgivesequation. Look at example x2 + 20x = 0
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Putting x in evidence, we will have:
x2 + 20x = 0
x (x + 20) = 0
Note that we have a product where the factors are x and x + 20. Also note that the result of this multiplication is equal to zero. So, for this result to be found, x must equal zero, or x + 20 must equal zero.
If x = 0, we already have one of the results of equationofseconddegree.
If x + 20 = 0, we will have:
x + 20 = 0
x = – 20
Therefore, the solution to this equation is:
S = {0, – 20}
Whenever C = 0, you can use this strategy to solve equationsofseconddegree. This method is much faster and requires fewer steps than the formulainBhaskara, however, will only solve quadratic equations where the coefficient c equals 0.
resolution formula
Using the same idea above for the general case where c = 0, we can determine a solving formula for the equationsofseconddegree that have this format. Watch:
ax2 + bx = 0
dividing the whole equation by "a", we will have:
ax2 + bx = 0
a a a
x2 + bx = 0
The
Putting x in evidence, we will have:
x (x + b/a) = 0
Note that x = 0 or x + b/a = 0. In the latter case, we will have:
x + B = 0
The
x = - B
The
So the solutions of a equationincomplete of seconddegree with C = 0 are:
x = 0 or x = – B
The
By Luiz Paulo Moreira
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
SILVA, Luiz Paulo Moreira. "Incomplete second degree equations with a null coefficient"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/equacoes-incompletas-segundo-grau-com-coeficiente-c-nulo.htm. Accessed on June 28, 2021.
