Explanation Given information: The algebraic expression involve letters a , b , c , … . Calculation: Consider the expression involves three letter, a b + c a c + b b c + a Thus, 2 + 1 = 3 So, 3 different expressions can be derived from three letters if letters are interchanged in all possible ways. Consider the expression involves four letter, a b + c d a c + b d a d + b c b c + a d b d + a c c d + a b Thus, 3 + 2 + 1 = 6 So, 6 different expressions can be derived from four letters if letters are interchanged in all possible ways. Similarly for 26 letters, 25 + 24 + … + 1 = 325 So, 325 different expressions can be derived from 26 letters if letters are interchanged in all possible ways. Consider the equation with degree one then, a x + c = 0 x = − c a Now, the equation with two degree, a x 2 + b x + c = 0 Now, the discriminant is, Δ = b 2 − 4 a c The general solution is, x = − b ± Δ 2 a For the equation with degree three, a x 3 + b x 2 + c x + d = 0 So, discriminant is, Δ = 18 a b c d − 4 b 3 d + b 2 c 2 − 4 a c 3 − 27 a 2 d 2 If, Δ > 0 There are three distinct roots. If, Δ = 0 The roots will be multiple and all real. If, Δ < 0 There will be one real root and two complex roots

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 11.8, Problem 60PS

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The number of different expressions that can be derived if the letters are interchange in all possible ways the general solution with degree 1, 2, and 3 .

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Chapter 11.8, Problem 59PS

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Chapter 11 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

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The number of different expressions that can be derived if the letters are interchange in all possible ways the general solution with degree 1 , 2 , and 3 .

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The number of different expressions that can be derived if the letters are interchange in all possible ways the general solution with degree 1, 2, and 3 .

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Chapter 11 Solutions