Explanation Procedure used: Procedure for Synthetic Division: “1. Write the coefficients of f ( x ) . Be certain that the powers are in descending order and that zeros are inserted for missing powers. 2. Carry down the left coefficient, then multiply it by r , and place this product under the second coefficient of the top line. 3. Add the two numbers in the second column and place the result below. Multiply this sum by r and place the product under the third coefficient of the top line. 4. Continue this process until the bottom row has as many numbers as the top row”. Calculation: It is given that r 1 = − 1 , r 2 = 1 4 r 3 = 1 3 are the roots of the equation 24 x 5 + 10 x 4 + 7 x 2 − 6 x + 1 = 0 . The powers of s are in descending order, write down the coefficient of f ( x ) = 24 x 5 + 10 x 4 + 7 x 2 − 6 x + 1 and zeros are inserted for missing powers and then place − 1 to the right end. 24 10 0 7 − 6 1 − 1 Bring down the left coefficient 24 to the bottom line and multiply it by –1, and place the product value –24 under the second coefficient 10 of the top line. Proceed in this similar manner, to find the quotient and remainder. 24 10 0 7 − 6 1 − 1 − 24 14 − 14 7 − 1 _ 24 − 14 14 − 7 1 0 1 4 6 − 2 3 − 1 _ 24 − 8 12 − 4 0

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 15, Problem 34RE

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The remaining roots of the equation 24x5+10x4+7x2−6x+1=0 using synthetic division.

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Chapter 15, Problem 33RE

Chapter 15, Problem 35RE

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The remaining roots of the equation 24 x 5 + 10 x 4 + 7 x 2 − 6 x + 1 = 0 using synthetic division.

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The remaining roots of the equation 24x5+10x4+7x2−6x+1=0 using synthetic division.

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