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Unformatted text preview: e box and λ is called a Lagrange multiplier. With the help of your classmates, solve the system.9 2y + 2z = λyz 2x + 2z = λxz 2y + 2x = λxy xyz = 1000 13. According to Theorem 3.16 in Section 3.4, the polynomial p(x) = x4 + 4 can be factored into the product linear and irreducible quadratic factors. In this exercise, we present a method for obtaining that factorization. (a) Show that p has no real zeros. (b) Because p has no real zeros, its factorization must be of the form (x2 + ax + b)(x2 + cx + d) where each factor is an irreducible quadratic. Expand this quantity and gather like terms together. (c) Create and solve the system of nonlinear equations which results from equating the coefficients of the expansion found above with those of x4 + 4. You should get four equations in the four unknowns a, b, c and d. Write p(x) in factored form. 14. Factor q (x) = x4 + 6x2 − 5x + 6. 9 If using λ bothers you, change it to w when you solve the system. 8.7 Systems of Non-Linear Equations and Inequalities 8.7.2 547 Answers √ 1. (a) (±2...
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