Complex Numbers
sqrt(-36)
6i
Solve:
x^2-25
+-5
Find the zeros of
P(x)=-2x^2-4x+6
-3 and 1
Given
P(x)=-x^3+5x^2-7x+1
Find P(2)
-1
Given
f(x)=3x^4+5x^3-35x^2-55x+22
Without a calculator, is there a zero between 3 & 4?
(Use Intermediate Value Theorem)
f(3)=-80
f(4)=330
YES
(8-7i)-(-12+2i)
20-9i
Solve:
6x^2-15x+6=0
{1/2, 2}
Find
(2x^4-x^3+4x^2-4x+3)/(2x-1)
x^3+2x-1+2/(2x-1)
The function
f(x)=x^6-5x^5+3x^4+x^3+40x^2-24x-72
Has a zero of 2 and -1, and a zero of 3 with multiplicity 2. Find all the other zeros of f.
-1+-isqrt(3)
Solve:
x^3+3x=0
f(x)={0, +-isqrt(3)}
i65
i
Solve:
x^2-4x=2
2+-sqrt(6)
A rocket is projected upward from a platform 3 feet high with an initial velocity of 64 feet/second. What will be the maximum height of the rocket?
s(t)=-16t^2+64t+s_0
67 feet
Find the local maximum of the function (x-value)
f(x)=-x^3+9x-4
sqrt(3)
Find a cubic polynomial f(x) in standard form with cubic coefficient 1 with zeroes of 4 and 2i, with f(1)=15
f(x)=x^3-4x^2+4x-16
2i(3-i)^2
12+16i
Solve:
3x^2+3x-20le0
[(-3-sqrt33)/6,(-3+sqrt33)/6]
The width of a rectangular box is 3 times its height, and its length is 11 inches more than its height. Find the dimensions of the box if its volume is 720 cubic inches.
15" x 12" x 4"
Given
f(x)=4x^4-21x^2-25
Find all zeroes
+-5/2, +-i
A rectangular piece of sheet metal is 20 inches wide. it is to be made into a rain gutter by turning up the edges to form parallel sides. Let x represent the length of each of the parallel sides in inches. What is the maximum area of the cross-section of the gutter?
50 square inches
(11+10i)/(2+3i)
4-i
Find the vertex of the quadratic function:
P(x)=-2x^2-4x+6
(-1,8)
Give the interval where this function is DECREASING:
2x^3-3x^2-12x+1
(-1,2)
After a 2 inch slice is cut off the top of a cube, the resulting solid has a volume of 32 cubic inches. What are the dimensions of the original cube?
4" x 4" x 4"
What is the maximum area rectangle that can be inscribed in a region bounded by the x-axis on the bottom and the parabola f(x)=9-x2 on the upper left and right?
sqrt3