Explanation Approach: Intermediate value theorem, Let P ( x ) be a polynomial function with real coefficients. If P ( a ) ≠ P ( b ) for a < b , then P ( x ) takes on all values between P ( a ) and P ( b ) on the closed interval [ a , b ] . By this theorem, P ( a ) and P ( b ) have opposite signs, the number 0 must lies between them. (i.e.) P ( x ) = 0 and x is the real zero of P ( x ) Calculation: Given, P ( x ) = 2 x 2 + x − 3 , − 2 and 1 We will evaluate the polynomial function at x = − 2 and x = − 1 The resulting values have opposite signs. To find the P ( − 2 ) and P ( − 1 ) P ( x ) = 2 x 2 + x − 3 ⋯ ( 1 ) P ( − 2 ) = 2 ( − 2 ) 2 + ( − 2 ) − 3 = 2 ( 4 ) − 2<

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ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 4.2, Problem 71E

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The polynomial function $P(x)=2x2+x−3$ has at least one real zero between the specified numbers.

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Chapter 4.2, Problem 70E

Chapter 4.2, Problem 72E

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The polynomial function P ( x ) = 2 x 2 + x − 3 has at least one real zero between the specified numbers.

Solution Summary: The author evaluates the polynomial function P(x) at x=-32.

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The polynomial function $P(x)=2x2+x−3$ has at least one real zero between the specified numbers.

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