Explanation Given information: The equation is 20 x ( x + 2 ) ( x − 1 ) = 5 x 3 − 24 x − 14 x 2 . Formula used: The principle of zero product states that, for a product of two factors to be zero, atleast one of the factors should be equal to zero. Mathematically, ( x − a ) ( x − b ) = 0 implies ( x − a ) = 0 or ( x − b ) = 0 . Calculation: Consider the equation, 20 x ( x + 2 ) ( x − 1 ) = 5 x 3 − 24 x − 14 x 2 Solve the equation as, 20 x ( x + 2 ) ( x − 1 ) = 5 x 3 − 24 x − 14 x 2 20 x ( x 2 + x − 2 ) = 5 x 3 − 24 x − 14 x 2 20 x 3 + 20 x 2 − 40 x = 5 x 3 − 24 x − 14 x 2 Rewrite the equation as, 20 x 3 + 20 x 2 − 40 x − 5 x 3 + 24 x + 14 x 2 = 0 Add the like terms as, 20 x 3 + 20 x 2 − 40 x − 5 x 3 + 24 x + 14 x 2 = 0 x 3 ( 20 − 5 ) + x 2 ( 20 + 14 ) + x ( − 40 + 24 ) = 0 15 x 3 + 34 x 2 − 16 x = 0 Find the factors by factorization method. 15 x 3 + 34 x 2 − 16 x = 0 x ( 15 x 2 + 40 x − 6 x − 16 ) = 0 x ( 5 x − 2 ) ( 8 x + 3 ) = 0 Since, the product of the factors is zero, either of the two products must be zero, this implies, x = 0 , ( 5 x − 2 ) = 0 or ( 8 x + 3 ) = 0 . Solve the factors further for x, 5 x − 2 = 0 5 x = 2 x = 2 5 Similarly, 8 x + 3 = 0 8 x = − 3 x = − 3 8 Now to check the solution substitute x = 0 in 15 x 3 + 34 x 2 − 16 x = 0

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Author: Marvin L. Bittinger, Judith A. Beecher

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Chapter 11, Problem 33T

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To calculate: The solution of the equation 20x(x+2)(x−1)=5x3−24x−14x2.

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Chapter 11, Problem 32T

Chapter 11, Problem 34T

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The solution of the equation 20 x ( x + 2 ) ( x − 1 ) = 5 x 3 − 24 x − 14 x 2 .

Solution Summary: The author explains the principle of zero product, which states that for a product of two factors to be zero, atleast one of the factors should be equal to zero.

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To calculate: The solution of the equation 20x(x+2)(x−1)=5x3−24x−14x2.

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Chapter 11 Solutions