The perimeter of a rectangle is 72 centimeters. The base is 2 times the height. What are the dimensions of the rectangle? a. h =
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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.
- <u>To visualize 5.3</u><u>7</u><u> more accurately, divide line segment between 5.37 and 5.38 in ten equal parts. 5.3</u><u>7</u><u> lies between 5.377 and 5.378.</u>
- <u>Again </u><u>use </u><u>divide</u><u> above portion between 5.377 and 5.378 into 10 equal parts, which shows 5.3</u><u>7</u><u> is located closer to 5.3778 than to 5.3777</u><u> </u><u>so </u><u>we </u><u>can </u><u>get </u><u>the </u><u>answer</u>
