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 = r 2 = − 3 is the repeated roots of the equation 4 n 4 + 28 n 3 + 61 n 2 + 42 n + 9 = 0 . The powers of n are in descending order, write down the coefficient of f ( n ) = 4 n 4 + 28 n 3 + 61 n 2 + 42 n + 9 and zeros are inserted for missing powers and then place − 3 to the right end. 4 28 61 42 9 − 3 Bring down the left coefficient 4 to the bottom line and multiply it by − 3 , and place the product value –12 under the second coefficient 28 of the top line. Proceed in this similar manner, to find the quotient and remainder. 4 28 61 42 9 − 3 − 12 − 48 − 39 − 9 _ 4 16 13 3 0 − 3 − 12 − 12 − 3 0 _ 4 4 1 0 0 The numbers presented in the last row denotes the coefficients of the quotient and the remainder. The quotient is 4 n 2 + 4 n + 1 and remainder is 0. Here, ( n + 3 ) , ( n + 3 ) and ( 4 n 2 + 4 n + 1 ) are factors of f ( n ) = 4 n 4 + 28 n 3 + 61 n 2 + 42 n + 9

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Chapter 15.2, Problem 16E

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The remaining roots of the equation 4n4+28n3+61n2+42n+9=0 using synthetic division.

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Chapter 15.2, Problem 15E

Chapter 15.2, Problem 17E

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The remaining roots of the equation 4 n 4 + 28 n 3 + 61 n 2 + 42 n + 9 = 0 using synthetic division.

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The remaining roots of the equation 4n4+28n3+61n2+42n+9=0 using synthetic division.

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Chapter 15 Solutions