Find all the zeros of f(x).
1 answer:
Answer:
-2, -1, -1, 1/3
Step-by-step explanation:
A graphing calculator can find the real roots of a polynomial pretty easily. The attached graph of this function shows its zeros to be ...
-2, -1, -1, 1/3
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The rational root theorem tells you that rational roots will be from the set ...
{±1/3, ±2/3, ±1, ±2}
Descarte's rule of signs tells you there will be 1 positive real root. The sum of coefficients is 24 (a relatively large positive number), so it is certain the positive root will be less than 1.
The sum of coefficients of odd-degree terms (11+1) is equal to the sum of coefficients of even-degree terms (3+11-2), telling you that -1 is a root. Synthetic division gives the cubic factor as 3x³ +8x² +3x -2, which has the same characteristics as the original quartic. That is, there is one positive real root, and -1 is a root of the cubic (hence a double root of f(x)).
Another round of synthetic division reveals the quadratic factor to be 3x² +5x -2, which can be factored as (x +2)(3x -1) to reveal the remaining roots.
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Answer: Surface area is equal to 200
Volume is equal to 333.33
Step-by-step explanation:
First, let's do surface area.
The surface area of a pyramid is equal to 1/2(perimeter of base)(lateral height) + area of the base
The perimeter of the base is 10(4) = 40; as the base is a square with a side length of 10.
The lateral height is given as 5 cm.
The area of the base is 10(10) = 100.
We can plug those numbers into the equation to get 1/2(40)(5) + 100, which comes out to be 200.
Now for volume.
The volume of a pyramid is equal to 1/3(area of the base)(height).
We already have the area of the base, which is 100.
The height is given as 10 cm.
Plugging those numbers into the equation, we get 1/3(100)(10), which is 1000/3 or about 333.33.
Hope this helps!