60. 321z+ 61.-2x3 + 5x2-3x+9=0 62. _x3 + 8x-12-0 Use the rational zero theorem,

Question

60. 321z+ 61.-2x3 + 5x2-3x+9=0 62. _x3 + 8x-12-0 Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in finding all real and imaginary root 0 to each equation. 63. x3-4x2-7x+10=0 64. x3 + 9x2 + 26x + 24 = 0 -65. r3-10x-3=0 66. 2x3-7x2 160 68. x4-4x3 + 7x2-16x + 12 = 0 69, 6' + 25x2-24x + 5 = 0 70·6x3-11x2-46x-24 0 --71. x4 + 2x3-3x2-4x+4-0 72, x5 + 3x3 + 2x=0 73. x4-6x3 + 12x2-8x=0 74, x4 + 9x3 + 27x2 + 27x = 0 i 75. 76. 2x7-2x6 + 7x5-7x4-4x3 + 4x2 0 77, 8x5 + 2x4-33x3 + 4x2 + 25x-6=0 78. 6x5 +x4-28x3-3x2 + 16x-4=0 F For each of the following functions use synthetic division and

Explanation / Answer

71) x^4 + 2x^3 - 3x^2 - 4x + 4 = 0

the rational zeros of the function are

+- { 1 , 2 , 4 }

= +- 1 , +- 2 , +- 4

checking the roots by plugging it in the equation

we get actual root at

x = 1 , x = -2

real roots are

x = 1 ( multiplicity 2 )

x = -2 ( multiplicity 2 )

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