The general form of the 2nd degree equation is ax² + bx + c = 0, where a, b and c are real numbers and a ≠ 0. Thus, the coefficients b and c can assume a value equal to zero, making the 2nd degree equation incomplete.
See some examples of complete and incomplete equations:
y2 + y + 1 = 0 (complete equation)
2x2 – x = 0 (incomplete equation, c = 0)
2t2 + 5 = 0 (incomplete equation, b = 0)
5x2 = 0 (incomplete equation b = 0 and c = 0)
Every second degree equation, whether incomplete or complete, can be solved using Bhaskara's equation:
Mind Map - Incomplete High School Equations
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Incomplete 2nd degree equations can be solved in another way. Look:
Coefficient b = 0
Any incomplete 2nd degree equation, which has the term b with a value equal to zero, can be solved by isolating the independent term. Note the following resolution:
4y2 – 100 = 0
4y2 = 100
y2 = 100: 4
y2 = 25
yy2 = √25
y’ = 5
y" = – 5
Coefficient c = 0
If the equation has the term c equal to zero, we use the factorization technique of the common term in evidence.
3x2 – x = 0 → x is a similar term in the equation, so we can put it in evidence.
x (3x – 1) = 0 → when we put a term in evidence we divide that term by the terms of the equation.
Now we have a product (multiplication) of two factors x and (3x – 1). The multiplication of these factors is equal to zero. For this equality to be true, one of the factors must equal zero. Since we don't know if it's the x or the (3x - 1), we equal the two to zero, forming two 1st degree equations, see:
x’ = 0 → we can say that zero is one of the roots of the equation.
and
3x -1 = 0
3x = 0 + 1
3x = 1
x’’ = 1/3 → is the other root of the equation.
Coefficient b = 0 and c = 0
In cases where the equation has coefficients b = 0 and c = 0, the roots of the incomplete 2nd degree equation are equal to zero. Note the following resolution:
4x2 = 0 → isolating the x we will have:
x2 = 0: 4
√x2 = √0
x = ± √0
x’ = x" = 0
by Mark Noah
Graduated in Mathematics
*Mental Map by Luiz Paulo Silva
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/equacao-2-grau-incompleta.htm