Solving Equations
#2 Solve:
x2 + 8x + 25 = 0
-4 +/- 3i
#1 What is the multiplicity of the zero (-3,0)?
f(x) = 3x4(x-1)2(x+3)5(x-3)3
5
#17: Find all real solutions of x4 - 4x3 + 12x - 9 = 0
x = 1, 3 +/- root3
#16 If one of the zeros of a quadratic function is 3+i, find the quadratic function
x2 - 6x + 10
#7 What is the vertex of the following quadratic function?
f(x) = x2 - 2x - 3
(1, -4)
#9 If you know that a quartic function has zeros 2+i and i, determine the other zeros
2-i and -i
#4 Write the expression in standard form:
(-4 - 3i) - (-8 + 2i)
4 - 5i
#23 Find the value for k given g(x) = x3 + 4x2 - kx + 8
k=-4
#22 Find the number of complex zeros for the follow equation:
f(x) = 2x5 - 7x4 + 10x3 - 5x2 - 2x + 2
5 (biggest exponent)
#5 Divide and write in standard form:
2/(1 + i)
1 - i
#10 Simplify using polynomial division:
(3x3 - x2 - 40x + 48)/(3x - 4)
x2 + x - 12
Write the quartic function f(x) in completely factored form that has zeros -2, -4, 3, and 0 and f(-1) = 4
1/3x(x+2)(x+4)(x-3)
#3 What is the maximum number of real zeros possible for the following function:
f(x) = 3x4 + ax3 - bx2 + 12x - 2
4 (number of sign changes in f(x) and f(-x))
#6 Simplify and write in standard form:
(1/i6) + i19
-1 - i
#15 Find the remainder when f(x) = x2001 - 3x53 + x2 + 2 is divided by x+1
5
#18 Given the following x and y values, find the linear model AND the quadratic model
x: 0, 1, 2, 3, 4, 5, 6
y: 7.62, 7.51, 7.56, 7.78, 8.16, 8.71, 9.43
linear: 0.30x + 7.21
quadratic: 0.083x2 - 0.197x + 7.62
#11 Find all the zeros of the function by factoring:
f(x) = x4 - 3x2 - 4
+/- 2, +/- i
#14 Find the cubic polynomial in factored form, irreducible over the reals, with the following zeros: -1, 1-i
f(x) = (x+1)(x2-2x+2)