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2 answers:
Answer:
See attachment
Step-by-step explanation:
The shaded boxes are where the new box is to be added.
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Step-by-step explanation:
A. Adding a square in the top left corner increases the perimeter. It removes one side and adds three. So the perimeter increases from 14 to 16.
B. Adding a square in the top center leaves the perimeter the same. It removes two sides but also adds two sides. So the perimeter is left at 14.
C. Adding a square to the bottom center decreases the perimeter. It removes three sides and adds one. So the perimeter decreases from 14 to 12.
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For this case we have that by definition, the discriminant of a quadratic expression is given by:
If the discriminant is less than zero then the expression has two different complex roots.
In this case we have the following expression:
So we have to:
The discriminant is given by:
Then, if we want two complex roots it must be fulfilled that:
Thus, the expression has two complex roots for all values greater than 4.
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