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 and r 2 = 2 are the roots of the equation x 4 − 10 x 3 + 35 x 2 − 50 x + 24 = 0 . The powers of x are in descending order, write down the coefficient of f ( x ) = x 4 − 10 x 3 + 35 x 2 − 50 x + 24 and zeros are inserted for missing powers and then place 1 to the right end. 1 − 10 35 − 50 24 1 Bring down the left coefficient 1 to the bottom line and multiply it by 1, and place the product value 1 under the second coefficient –10 of the top line. Proceed in this similar manner, to find the quotient and remainder. 1 − 10 35 − 50 24 1 1 − 9 26 − 24 _ 1 − 9 26 − 24 0 2 [ ∵ r 2 = 2 also a root ] 2 − 14 24 0 _ 1 − 7 12 0 0 The numbers presented in the last row denotes the coefficients of the quotient and the remainder

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 15, Problem 27RE

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The remaining roots of the equation x4−10x3+35x2−50x+24=0 using synthetic division.

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Chapter 15, Problem 26RE

Chapter 15, Problem 28RE

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Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

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The remaining roots of the equation x 4 − 10 x 3 + 35 x 2 − 50 x + 24 = 0 using synthetic division.

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The remaining roots of the equation x4−10x3+35x2−50x+24=0 using synthetic division.

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Chapter 15 Solutions