Depressed equation
equation resulting from reducing the number of roots in an equation
A depressed equation is a type of equation that is missing a term that is usually present in similar equations. In particular, a depressed equation is a polynomial equation of degree two that does not have a linear term (i.e., a first degree term with a non-zero coefficient).
The general form of a depressed equation is:
ax^2 + c = 0
where a and c are constants, and x is the variable.
To solve a depressed equation, we can use the quadratic formula, which is:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
where b is the coefficient of the missing linear term, sqrt denotes the square root function, and the ± symbol indicates that there are two possible solutions (corresponding to the two roots of the quadratic equation).
For example, if we have the depressed equation:
2x^2 – 8 = 0
we can use the quadratic formula to find the solutions:
x = (-b ± sqrt(b^2 – 4ac)) / 2a
x = (0 ± sqrt(0^2 – 4(2)(-8))) / 2(2)
x = (± sqrt(64)) / 4
x = ± 4 / 4
x = ± 1
Therefore, the solutions to the depressed equation 2x^2 – 8 = 0 are x = 1 and x = -1.
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