Is the question asking to see if x = 1, y=-2, and z=2 by solving the three equations?
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Answer:
Step-by-step explanation:
A direct variation equation has the form:
Where <em>k</em> is a constant.
By definition, we know that the perimeter of the square is the sum of the lengths of its sides or, as all the sides are equal, you can multiply the lenght of any side by 4.
Then, knowing that <em>y</em> is the dependent value and <em>x</em> the independent value and the constant <em>k=4, </em> you can write the following direct variation equation that represents the situation.
The general form of a quadratic (second degree) equation is
, where
is called the Discriminant.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
, a=1, b=-5, c=7
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.
The Discriminant determines how many roots the equation will have as follows:
i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.
In our equation,
so the discriminant is D=(-5)^2-4*1*7=25-28<0
Thus the equation has no roots.
Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.