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The first midterm exam for math 100, taught by dr. Sandy rutherford, held on october 6, 2004. The exam covers topics such as rational and irrational numbers, solving equations, polynomial factorization, cubic equations, and function analysis. Students are required to show their work and provide reasons for their answers. No calculators, notes, or textbooks are allowed.
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Instructor: Dr. Sandy Rutherford Date: October 6, 2004 Time: 11:30 – 12:
Name (please print):
Signature:
Student Number:
Question Mark Total Marks
Total 45
(a)
x + 3
(b) x^2 =
x^2 − 2
x^3 + x^2 + ax = 0 , where a is a real number.
Determine for which values of a this equation has 0,1,2, or 3 real solutions. Can it ever have more than 3 solutions? Explain.
(a) p(x) = x^4 + 2x^2 − 8
(b) q(x) =
x^2 + (^) x^1 x + (^) x^12
For this function, state the domain and range both before and after any continuous extension.