141 Concept Check Answer each question. 92. Show that the discriminant for the equation 22x2 + 5x - 322 = 0 is 49. If this equation is completely solved, it can be shown that the solution set is E -322, 22 2 F. We have a discriminant that is positive and a perfect square, yet the two solutions are irrational. Does this contradict the discussion in this section? 93. Is it possible for the solution set of a quadratic equation with integer coefficients to consist of a single irrational number? 94. Is it possible for the solution set of a quadratic equation with real coefficients to consist of one real number and one nonreal complex number? Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) 95. 4, 5 96. -3, 2 97. 1 + 22, 1 - 22 98. i, -i 1. Solve the linear equation 31x - 52 + 2 = 1 - 14 + 2x2. 2. Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. (a) 4x - 5 = -213 - 2x2 + 3 (b) 5x - 9 = 51-2 + x2 + 1 (c) 5x - 4 = 316 - x2 3. Solve the equation ay + 2x = y + 5x for y. (Assume a≠1.) 4. Earning Interest Johnny deposits some money at 2.5% annual interest and twice as much money at 3.0%. Find the amount deposited at each rate if his total annual interest income is $850. 5. (Modeling) Minimum Hourly Wage One model for the minimum hourly wage in the state of Missouri for the period 2013–2019 is y = 0.1607x - 316.2, where x represents the year and y represents the wage, in dollars. (Data from U.S. Department of Labor.) The actual 2015 minimum wage was $7.65. What does this model predict as the wage, to the nearest cent? What is the difference between the actual wage and the predicted wage? 6. Write4 + 2-24 8 in standard form a + bi. 7. Write the quotient 7 - 2i 2 + 4i in standard form a + bi. Chapter 1 Quiz (Sections 1.1–1.4) Solve each equation. 8. 3x2 - x = -1 9. x2 - 29 = 0 10. = 1 2 r2u, for r CHAPTER 1 Quiz
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