How many zeros does the function f(x) = 2x14 − 14x6 27x3 − 13x 12 have?
2 answers:
Answer:
The function f(x) has 14 zeros.
Step-by-step explanation:
We know that by Fundamental Theorem of Algebra :
Any polynomial equation of degree n with complex coefficient has exactly 'n' complex roots counting multiplicity.
Here we are given a polynomial function f(x) as:
So, this polynomial function is of degree 14.
Hence, the given polynomial function f(x) has exactly 14 zeros.
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Answer:
and
.
Step-by-step explanation:
Please find the attachment.
We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.
The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:
We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:
Let us find area of window equation as:
Now, we will solve for L is terms W from perimeter equation as:
Substitute this value in area equation:
Since we need the area of window to maximize, so we need to optimize area equation.
Let us find derivative of area equation as:
To find maxima, we will equate first derivative equal to 0 as:
Upon substituting in equation
, we will get:
Therefore, the dimensions of the window that will maximize the area would be and
.
