57 25x250x 75 58 10x 59Y3y24y 0 60 61 3z3 6z272z 63 x4 36x

57. 25x2-50x 75 58. 10x- 59-Y-3y2-4y = 0 60 61. 3z3 + 6z2-72z 63. x4 36x20 65. r4 + 6p3 = 7p2 67. x4-13x-=-36 68. x4-1 69, x4 + 1 2x2 71. a 81 73.jrs_2x2 _ x + 2 = 0 74. x3-x2 + 4x-4 = 0 2 . y3 3 62. 4Z3 64. 4x4 = 66. r43 70. x4-8 72. b3 = .3 76. 3x3 + 2x2-27x-18 0

Solution

61. 3z³ + 6z² = 72z

=> z³ + 2z² = 24z

=> z( z² + 2z - 24 ) = 0

=> z[ z² + (6 - 4)z - 24 ] = 0

=> z [ z(z+6) - 4(z+6) ]=0

=> z(z+6)(z-4) = 0

z = 0 , z = - 6 , z = 4 .

73. x³ - 2x² - x +2 = 0

=> x²(x-2) - 1(x -2) = 0

=> (x² - 1)(x - 2) = 0

=> (x + 1)(x - 1)(x - 2) = 0

roots are x = -1 , x = 1 , x = 2

75. x³ - 5x² + x - 5 = 0

=> x²(x -5 ) + 1(x - 5) = 0

=> (x² + 1)(x - 5) = 0

=> (x² - (-i)²)(x - 5) = 0

=> ( x + i)(x - i)(x-5) = 0

=> x = -i , x = i , x = 5 .