59) 60) Which equation has the roots 3 + x/i and 3 x/i ? 61) 62) 63) A)x2-?x-4=0 C)x2+6x+7=0 B)x2-6x+7=0 D)x2-7x+6=0 Which equation has roots whose sum is 3 and whose product is 4? A)x2+3x4=0 C)x2+4x3=0 B)xz-4x+3=0 D):r2-3.r-4=0 Write an equation in the form (1.12 + bx + c = 0 if the sum of the roots is S and the product of the roots is 3. [Show all work] Write an equation in the form of + bx + c = 0 if the sum of the roots is -4 and the product of the roots is 5. [Show of! work] 20922CBS V1 - Page T 64) Write an equation in the form axz + bx + o = 0 if the sum of the roots is 4 and the product of the roots is 0. [Show a}! work] 65) Write an equation in the form axz + bx + c = 0 if the sum of the roots is g and the product of the roots is 2 [Show all work] 66] Write an equation in the form 0x2 + bx + c = 0 if the sum of the roots is -% and the product of the roots is %. [Show of} work] 67) Write an equation in the form (1:2 + bx + c = 0 if the sum of the roots is -% and the product of the roots is g [Show all work] 63) [f the roots of a quadratic equation are 5 and 3, write the equation in ax2 + bx + c = 0 form. [Show a\" work] 69) If the roots of a quadratic equation are -8 and 3, write the equation in to:2 + bx + c = 0 form. [Show of! work] 70) 1f the roots of a quadratic equation are -'7 and -5. write the equation in w:2 + bx + c = 0 form. [Show a\" work] 7 I) If the roots of a quadratic equation are -% and - %, write the equation in tax2 + bx + c = 0 form. [Show a}! work] 72) If the roots of a quadratic equation are W and - , write the equation in ax2 + bx + c = 0 form. [Show all work] 73) If the roots of a quadratic equation are -2 + \\/5 and -2 - x/E, write the equation in axz + bx + c = 0 form. [Show all work] 20922038 v1 - Page 8 3+2\"! and 74) [f the roots of a quadratic equation are write the equation in ax: + bx + c = 0 form. [Show a\" work] 75) If a quadratic equation has n = 3 and r2 = 6 as roots: (a) Find the sum of the roots. [Show a}! work] (b) Find the product of the roots. [Show a}! work] (c) Write the quadratic equation with integral coefcients having these roots. [Show all work] 76) If a quadratic equation has r] = % and r2 = g as roots: (a) Find the sum of the roots. [Show all work] (b) Find the product of the roots. [Show all work] (c) Write the quadratic equation with integral coefcients having these roots. [Show all work] 20922CB8 V1 - Page 9 77) If a quadratic equation has 1 = -, and r2 = = as 80) The roots of 6x2(x + 8) + 5x(x + 8) = 0 are roots: A) 8, 0, 5 C) - 6, 0, (a) Find the sum of the roots. [Show all work. ] B) -8, 0, -2 D) S, -8 (b) Find the product of the roots. [Show all work. ] (c) Write the quadratic equation with integral coefficients having these roots. [Show all work. ] 81) How many real roots does the equation x(x2 - 4) (2x - 3) = 0 have? A) 1 B) 2 C 3 D) 4 78) If a quadratic equation has /1 = 4 -2v7 and 12 = 4 + 2v7 as roots: (a) Find the sum of the roots. [Show all work. ] (b) Find the product of the roots. [Show all 82) Which values of x are solutions of the equation x' + x2 - 2x = 0? work.] (c) Write the quadratic equation with integral A) 0, -1, 2 C) 0, 1, 2 coefficients having these roots. [Show all B) 0, -1, -2 D) 0, 1, -2 work.] Questions 83 through 94 refer to the following: 79) The roots of 24x3 = 10x2 + 4x are Solve the given polynomial equation by factoring and/or using the Quadratic Formula. [Show all work. ] A) -4, 2 [Express all real roots in simplest form. ] B) -1, 0, 3 D) 1, 0, 3 83) x5 - 10x3 + 21x = 0 84) (x + 2) (x2 + 5x - 7) = 020922CB8 V1 - Page 10 85) x4 = 29x2 - 100 92) (3x2 + 13x - 10) (12 + 3x + 1) = 0 86) 2x3 = 3x - 5x2 93 ) (3x2 + 5x + 2)(x2 - 3x + 1) = 0 87) 3x3 + 5x2 =x 94) x4 - 8x2 + 15 = 0 88) 4x3 + 5x = 13x2 95) Solve the equation 8x3 + 4x2 - 18x - 9 = 0 algebraically for all values of x. [Show all work. ] 89) 3x3 - 5x2 + x= 0 96) Use graphing technology, determine the real roots of x2 - 5x2 + 16x - 12 = 0, correct to the nearest tenth. 90) (x2 - 4) (x2 + 3x - 6) = 0 97) Using graphing technology, determine the roots of x - 3x2 - 11x + 24 = 0, correct to the nearest tenth. 91) (2x - 1)(3x2 - 4x - 1) = 098) The equation whose roots are 2 + v-1, 2 - 102) Which one of the following is a polynomial V-1 and -5 is equation with integer coefficients and roots of - -, 2, and 3? A) x3 + x2 - 15x + 25 = 0 B) x3 - 21x2 + 3x - 10 = 0 A) 2x3 + 9x2 + 13x - 6=0 C) x5 + 3x2 - 2x + 15=0 B) 2x3 - 9x2 - 13x - 6= 0 D) x3 - 2x2 + 15x - 15 = 0 C) 2x3 - 9x2 + 7x + 6=0 D) 2x3 - 9x2 - 13x + 6=0 99) Which one of the following is a polynomial equation whose roots are +1 and +2? 103) Write a polynomial equation (with integral coefficients of lowest degree) that has roots of A) x 4 + 4=0 C) x4 - 1=0 -3, 0, and 3. [Show all work. ] B)x4 - 5x2 + 4= 0 D) x4 + 5x2 + 4= 0 104) The remainder when x3 - 3x2 + 15x - 20 is 100) Which one of the following polynomial divided by x - 3 is equations has roots of +v 3 and + v5? A) -119 B) 65 C) -15 D) 25 A) x3 + 8x2+ 15 =0 C)x4 -8x2+ 15=0 B) x2 - 15 = 0 D) x4 - 2x2 - 15 = 0 105) The remainder when 3x3 - 2x2 - 10x + 9 is divided by x - 2 is 101) Which one of the following is a polynomial equation with integer coefficients and roots of 1, A) - 3 B) -5 C) 5 D) 3 z, and -? A) 8x3 - 14x2 + 7x - 1= 0 B) 8x3 - 14x2 + 7x + 1= 0 C) 8x3 - 14x2 - 7x - 1 =0 106) The remainder when x3 - 5x2 + 3x - 1 is divided D) x3 - 14x2 + 2x + 1=0 by x - 1 is A) -2 B) 2 C) -10 DO20922CB8 V1 - Page 12 107) What is the remainder when the polynomial 110) Determine an equation of a polynomial function x* + 3x - x + 8 is divided by x + 2? of lowest degree whose zeros are 3, -2, and -2. A) -4 B) 44 C) -44 D) 4 A) f(x) = x3+x2+ 8x+ 12 B) f( x) = x3 + x2 - 8x - 12 C) f( x ) = x3 + x2 + 8x -12 D) f(x) = x+x - 8x+12 108) Determine the remainder when the polynomial x4 - 3x3 - x2 + 8 is divided by x + 2 . A) -44 B) 44 C) 4 D) -4 111) Determine an equation of a polynomial function of lowest degree with integer coefficients that has x-intercepts of 1, -2, and -3. A) f(x ) = x3 + 4x2+x+6 109) Use the Remainder Theorem to find the B) f(x ) = x3 - 4x2 + x - 6 remainder when f(x) = x#+ 2x + x2 + 5x - 8 is C) f( x) = x3+ 4x2 +x - 6 divided by x + 3. [Show all work. ] D) f(x) = x3 - 4x2 - x+6 112) An equation of a quadratic function having x-intercepts of -4 and 3 is A) f(x) = x2 - x+ 12 C) f(x) =x2 - 7x -12 B) f(x ) = x2+ 7x+ 12 D) f(x) =x2+x-12