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Found: 2

Problem #PRU-61014

Problems Algebra Polynomials Polynomials(other) Calculus Real numbers Rational and irrational numbers

13–15 3.0

Derive from the theorem in question 61013 that $\sqrt{17}$ is an irrational number.

Problem #PRU-78003

Problems Number Theory Divisibility Arithmetic functions Algebra Polynomials Polynomials(other)

15–16 3.0

Prove that if $x_{0}^{4} + a_{1} x_{0}^{3} + a_{2} x_{0}^{2} + a_{3} x_{0} + a_{4}$ and $4 x_{0}^{3} + 3 a_{1} x_{0}^{2} + 2 a_{2} x_{0} + a_{3} = 0$ then $x^{4} + a_{1} x^{3} + a_{2} x^{2} + a_{3} x + a_{4}$ is divisible by $(x - x_{0})^{2}$ .