10.2 Exercises Do the exercises, and check your work. Mixed Exercises: Objectives 2 and 3 Find the error in each, and correct the mistake. 1) The solution to ax2 bx c 0 (a 0) can be found using the quadratic formula. x b 2b2 4ac 2a 2) In order to solve 5n2 3n 1 using the quadratic formula, a student substitutes a, b, and c into the formula in this way: a 5, b 3, c 1. n (3) 2(3)2 4(5)(1) 2(5) 3) 2 6111 2 1 6111 4) The discriminant of 3z2 4z 1 0 is 2b2 4ac 2(4)2 4(3)(1) 216 12 24 2. Objective 2: Solve a Quadratic Equation Using the Quadratic Formula Solve using the quadratic formula. 5) x2 4x 3 0 6) v2 8v 7 0 7) 3t2 t 10 0 8) 6q2 11q 3 0 9) k2 2 5k 10) n2 5 3n 11) y2 8y 25 12) 4x 5 x2 13) 3 2w 5w2 14) 2d 2 4 5d 15) r2 7r 0 16) p2 10p 0 17) 2k(k 3) 3 18) 3v(v 3) 7v 4 19) (2c 5)(c 5) 3 20) 11 (3z 1)(z 5) 21) 1 6 u2 4 3 u 5 2 22) 1 6 h 1 2 3 4 h2 23) 2(p 10) (p 10)(p 2) 24) (t 8)(t 3) 3(3 t) 25) 4g2 9 0 26) 25q2 1 0 27) x(x 6) 34 28) c(c 4) 22 29) (2s 3)(s 1) s2 s 6 30) (3m 1)(m 2) (2m 3)(m 2) 31) 3(3 4y) 4y2 32) 5a(5a 2) 1 33) 1 6 2 3 p2 1 2 p 34) 1 2 n 3 4 n2 2 35) 4q2 6 20q 36) 4w2 6w 16 37) Let f (x) x2 6x 2. Find x so that f (x) 0. 38) Let g(x) 3x2 4x 1. Find x so that g(x) 0. 39) Let h(t) 2t2 t 7. Find t so that h(t) 12. 40) Let P(a) a2 8a 9. Find a so that P(a) 3. 41) Let f (x) 5x2 21x 1 and g(x) 2x 3. Find all values of x such that f (x) g(x). 42) Let F(x) x2 3x 2 and G(x) x2 12x 6. Find all values of x such that F(x) G(x). Objective 3: Determine the Number and Type of Solutions of a Quadratic Equation Using the Discriminant 43) If the discriminant of a quadratic equation is zero, what do you know about the solutions of the equation? 44) If the discriminant of a quadratic equation is negative, what do you know about the solutions of the equation? Find the value of the discriminant. Then, determine the number and type of solutions of each equation. Do not solve. 45) 10d2 9d 3 0 46) 3j 2 8j 2 0 47) 4y2 49 28y 48) 3q 1 5q2 49) 5 u(u 6) 50) g2 4 4g 51) 2w2 4w 5 0 52) 3 2p2 7p 0 Find the value of a, b, or c so that each equation has only one rational solution. 53) z2 bz 16 0 54) k2 bk 49 0 55) 4y2 12y c 0 56) 25t2 20t c 0 57) ap2 12p 9 0 58) ax2 6x 1 0 Objective 4: Solve an Applied Problem Using the Quadratic Formula Write an equation, and solve. 59) One leg of a right triangle is 1 in. more than twice the other leg. The hypotenuse is 129 in. long. Find the lengths of the legs. 60) The hypotenuse of a right triangle is 134 in. long. The length of one leg is 1 in. less than twice the other leg. Find the lengths of the legs. www.mhhe.com/messersmith SECTION 10.2 The Quadratic Formula 631
messersmith_power_intermediate_algebra_1e_ch4_7_10
To see the actual publication please follow the link above