Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Concept explainers

Roots
The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form o…
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Chapter A.6, Problem 122AYU
To determine

To find: To show that product of roots of a quadratic equation is ca

Expert Solution & Answer
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Answer to Problem 122AYU

The product of roots of a quadratic equation is ca .

Explanation of Solution

Given information:

A quadratic equation of the form ax2+bx+c=0 .

Calculation:

Write the formula to calculate roots of a quadratic equation of the given form.

  x=−b±b2−4ac2a .

To find the product of these roots multiply them together.

  =−b+b2−4ac2a×−b−b2−4ac2a=b2−(b2−4ac)24a2=b2−b2+4ac4a2=4ac4a2

  =ca

Thus it is verified.

Therefore, the product of roots of a quadratic equation is ca .

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Chapter A Solutions

Precalculus

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A.7 - Prob. 11AYUCh. A.7 - Prob. 12AYUCh. A.7 - Prob. 13AYUCh. A.7 - Prob. 14AYUCh. A.7 - Prob. 15AYUCh. A.7 - Prob. 16AYUCh. A.7 - Prob. 17AYUCh. A.7 - Prob. 18AYUCh. A.7 - Prob. 19AYUCh. A.7 - Prob. 20AYUCh. A.7 - Prob. 21AYUCh. A.7 - Prob. 22AYUCh. A.7 - Prob. 23AYUCh. A.7 - Prob. 24AYUCh. A.7 - Prob. 25AYUCh. A.7 - Prob. 26AYUCh. A.7 - Prob. 27AYUCh. A.7 - Prob. 28AYUCh. A.7 - Prob. 29AYUCh. A.7 - Prob. 30AYUCh. A.7 - Prob. 31AYUCh. A.7 - Prob. 32AYUCh. A.7 - Prob. 33AYUCh. A.7 - Prob. 34AYUCh. A.7 - Prob. 35AYUCh. A.7 - Prob. 36AYUCh. A.7 - Prob. 37AYUCh. A.7 - Prob. 38AYUCh. A.7 - Prob. 39AYUCh. A.7 - Prob. 40AYUCh. A.7 - Prob. 41AYUCh. A.7 - Prob. 42AYUCh. A.7 - Prob. 43AYUCh. A.7 - Prob. 44AYUCh. A.7 - Prob. 45AYUCh. A.7 - Prob. 46AYUCh. A.7 - Prob. 47AYUCh. A.7 - Prob. 48AYUCh. A.7 - Prob. 49AYUCh. A.7 - Prob. 50AYUCh. A.7 - Prob. 51AYUCh. A.7 - Prob. 52AYUCh. A.7 - Prob. 53AYUCh. A.7 - Prob. 54AYUCh. A.7 - Prob. 55AYUCh. A.7 - Prob. 56AYUCh. A.7 - Prob. 57AYUCh. A.7 - Prob. 58AYUCh. A.7 - Prob. 59AYUCh. A.7 - Prob. 60AYUCh. A.7 - Prob. 61AYUCh. A.7 - Prob. 62AYUCh. A.7 - Prob. 63AYUCh. A.7 - Prob. 64AYUCh. A.7 - Prob. 65AYUCh. A.7 - Prob. 66AYUCh. A.7 - Prob. 67AYUCh. A.7 - Prob. 68AYUCh. A.7 - Prob. 69AYUCh. A.7 - Prob. 70AYUCh. A.7 - Prob. 71AYUCh. A.7 - Prob. 72AYUCh. A.7 - Prob. 73AYUCh. A.7 - Prob. 74AYUCh. A.7 - Prob. 75AYUCh. A.7 - Prob. 76AYUCh. A.7 - Prob. 77AYUCh. A.7 - Prob. 78AYUCh. A.7 - Prob. 79AYUCh. A.7 - Prob. 80AYUCh. A.7 - Prob. 81AYUCh. A.7 - Prob. 82AYUCh. A.7 - Prob. 83AYUCh. A.7 - Prob. 84AYUCh. A.7 - Prob. 85AYUCh. A.7 - Prob. 86AYUCh. A.7 - Prob. 87AYUCh. A.7 - Prob. 88AYUCh. A.7 - Prob. 89AYUCh. A.7 - Prob. 90AYUCh. A.7 - Prob. 91AYUCh. A.7 - Prob. 92AYUCh. A.7 - Prob. 93AYUCh. A.7 - Prob. 94AYUCh. A.8 - Prob. 1AYUCh. A.8 - Prob. 2AYUCh. A.8 - Prob. 3AYUCh. A.8 - Prob. 4AYUCh. A.8 - Prob. 5AYUCh. A.8 - Prob. 6AYUCh. A.8 - Prob. 7AYUCh. A.8 - Prob. 8AYUCh. A.8 - Prob. 9AYUCh. A.8 - Prob. 10AYUCh. A.8 - Prob. 11AYUCh. A.8 - Prob. 12AYUCh. A.8 - Prob. 13AYUCh. A.8 - Prob. 14AYUCh. A.8 - Prob. 15AYUCh. A.8 - Prob. 16AYUCh. A.8 - Prob. 17AYUCh. A.8 - Prob. 18AYUCh. A.8 - Prob. 19AYUCh. A.8 - Prob. 20AYUCh. A.8 - Prob. 21AYUCh. A.8 - Prob. 22AYUCh. A.8 - Prob. 23AYUCh. A.8 - Prob. 24AYUCh. A.8 - Prob. 25AYUCh. A.8 - Prob. 26AYUCh. A.8 - Prob. 27AYUCh. A.8 - Prob. 28AYUCh. A.8 - Prob. 29AYUCh. A.8 - Prob. 30AYUCh. A.8 - Prob. 31AYUCh. A.8 - Prob. 32AYUCh. A.8 - Prob. 33AYUCh. A.8 - Prob. 34AYUCh. A.8 - Prob. 35AYUCh. A.8 - Prob. 36AYUCh. A.8 - Prob. 37AYUCh. A.8 - Prob. 38AYUCh. A.8 - Prob. 39AYUCh. A.8 - Prob. 40AYUCh. A.8 - Prob. 41AYUCh. A.8 - Prob. 42AYUCh. A.8 - Prob. 43AYUCh. A.8 - Prob. 44AYUCh. A.8 - Prob. 45AYUCh. A.8 - Prob. 46AYUCh. A.8 - Prob. 47AYUCh. A.8 - Prob. 48AYUCh. A.8 - Prob. 49AYUCh. A.8 - Prob. 50AYUCh. A.8 - Prob. 51AYUCh. A.8 - Prob. 52AYUCh. A.8 - Prob. 53AYUCh. A.8 - Prob. 54AYUCh. A.8 - Prob. 55AYUCh. A.8 - Prob. 56AYUCh. A.8 - Prob. 57AYUCh. A.8 - Prob. 58AYUCh. A.8 - Prob. 59AYUCh. A.8 - Prob. 60AYUCh. A.8 - Prob. 61AYUCh. A.9 - Prob. 1AYUCh. A.9 - Prob. 2AYUCh. A.9 - Prob. 3AYUCh. A.9 - Prob. 4AYUCh. A.9 - Prob. 5AYUCh. A.9 - Prob. 6AYUCh. A.9 - Prob. 7AYUCh. A.9 - Prob. 8AYUCh. A.9 - Prob. 9AYUCh. A.9 - Prob. 10AYUCh. A.9 - Prob. 11AYUCh. A.9 - Prob. 12AYUCh. A.9 - Prob. 13AYUCh. A.9 - Prob. 14AYUCh. A.9 - Prob. 15AYUCh. A.9 - Prob. 16AYUCh. A.9 - Prob. 17AYUCh. A.9 - Prob. 18AYUCh. A.9 - Prob. 19AYUCh. A.9 - Prob. 20AYUCh. A.9 - Prob. 21AYUCh. A.9 - Prob. 22AYUCh. A.9 - Prob. 23AYUCh. A.9 - Prob. 24AYUCh. A.9 - Prob. 25AYUCh. A.9 - Prob. 26AYUCh. A.9 - Prob. 27AYUCh. A.9 - Prob. 28AYUCh. A.9 - Prob. 29AYUCh. A.9 - Prob. 30AYUCh. A.9 - Prob. 31AYUCh. A.9 - Prob. 32AYUCh. A.9 - Prob. 33AYUCh. A.9 - Prob. 34AYUCh. A.9 - Prob. 35AYUCh. A.9 - Prob. 36AYUCh. A.9 - Prob. 37AYUCh. A.9 - Prob. 38AYUCh. A.9 - Prob. 39AYUCh. A.9 - Prob. 40AYUCh. A.9 - Prob. 41AYUCh. A.9 - Prob. 42AYUCh. A.9 - Prob. 43AYUCh. A.9 - Prob. 44AYUCh. A.9 - Prob. 45AYUCh. A.9 - Prob. 46AYUCh. A.9 - Prob. 47AYUCh. A.9 - Prob. 48AYUCh. A.9 - Prob. 49AYUCh. A.9 - Prob. 50AYUCh. A.9 - Prob. 51AYUCh. A.9 - Prob. 52AYUCh. A.9 - Prob. 53AYUCh. A.9 - Prob. 54AYUCh. A.9 - Prob. 55AYUCh. A.9 - Prob. 56AYUCh. A.9 - Prob. 57AYUCh. A.9 - Prob. 58AYUCh. A.9 - Prob. 59AYUCh. A.9 - Prob. 60AYUCh. A.9 - Prob. 61AYUCh. A.9 - Prob. 62AYUCh. A.9 - Prob. 63AYUCh. A.9 - Prob. 64AYUCh. A.9 - Prob. 65AYUCh. A.9 - Prob. 66AYUCh. A.9 - Prob. 67AYUCh. A.9 - Prob. 68AYUCh. A.9 - Prob. 69AYUCh. A.9 - Prob. 70AYUCh. A.9 - Prob. 71AYUCh. A.9 - Prob. 72AYUCh. A.9 - Prob. 73AYUCh. A.9 - Prob. 74AYUCh. A.9 - Prob. 75AYUCh. A.9 - Prob. 76AYUCh. A.9 - Prob. 77AYUCh. A.9 - Prob. 78AYUCh. A.9 - Prob. 79AYUCh. A.9 - Prob. 80AYUCh. A.9 - Prob. 81AYUCh. A.9 - Prob. 82AYUCh. A.9 - Prob. 83AYUCh. A.9 - Prob. 84AYUCh. A.9 - Prob. 85AYUCh. A.9 - Prob. 86AYUCh. A.9 - Prob. 87AYUCh. A.9 - Prob. 88AYUCh. A.9 - Prob. 89AYUCh. A.9 - Prob. 90AYUCh. A.9 - Prob. 91AYUCh. A.9 - Prob. 92AYUCh. A.9 - Prob. 93AYUCh. A.9 - Prob. 94AYUCh. A.9 - Prob. 95AYUCh. A.9 - Prob. 96AYUCh. A.9 - Prob. 97AYUCh. A.9 - Prob. 98AYUCh. A.9 - Prob. 99AYUCh. A.9 - Prob. 100AYUCh. A.9 - Prob. 101AYUCh. A.9 - Prob. 102AYUCh. A.9 - Prob. 103AYUCh. A.9 - Prob. 104AYUCh. A.9 - Prob. 105AYUCh. A.9 - Prob. 106AYUCh. A.9 - Prob. 107AYUCh. A.9 - Prob. 108AYUCh. A.9 - Prob. 109AYUCh. A.9 - Prob. 110AYUCh. A.9 - Prob. 111AYUCh. A.9 - Prob. 112AYUCh. A.9 - Prob. 113AYUCh. A.9 - Prob. 114AYUCh. A.9 - Prob. 115AYUCh. A.9 - Prob. 116AYUCh. A.9 - Prob. 117AYUCh. A.9 - Prob. 118AYUCh. A.9 - Prob. 119AYUCh. A.9 - Prob. 120AYUCh. A.9 - Prob. 121AYUCh. A.9 - Prob. 122AYUCh. A.9 - Prob. 123AYUCh. A.9 - Prob. 124AYUCh. A.9 - Prob. 125AYUCh. A.9 - Prob. 126AYUCh. A.9 - Prob. 127AYUCh. A.9 - Prob. 128AYUCh. A.9 - Prob. 129AYUCh. A.9 - Prob. 130AYUCh. A.9 - Prob. 131AYUCh. A.10 - Prob. 1AYUCh. A.10 - Prob. 2AYUCh. A.10 - Prob. 3AYUCh. A.10 - Prob. 4AYUCh. A.10 - Prob. 5AYUCh. A.10 - Prob. 6AYUCh. A.10 - Prob. 7AYUCh. A.10 - Prob. 8AYUCh. A.10 - Prob. 9AYUCh. A.10 - Prob. 10AYUCh. A.10 - Prob. 11AYUCh. A.10 - Prob. 12AYUCh. A.10 - Prob. 13AYUCh. A.10 - Prob. 14AYUCh. A.10 - Prob. 15AYUCh. A.10 - Prob. 16AYUCh. A.10 - Prob. 17AYUCh. A.10 - Prob. 18AYUCh. A.10 - Prob. 19AYUCh. A.10 - Prob. 20AYUCh. A.10 - Prob. 21AYUCh. A.10 - Prob. 22AYUCh. A.10 - Prob. 23AYUCh. A.10 - Prob. 24AYUCh. A.10 - Prob. 25AYUCh. A.10 - Prob. 26AYUCh. A.10 - Prob. 27AYUCh. A.10 - Prob. 28AYUCh. A.10 - Prob. 29AYUCh. A.10 - Prob. 30AYUCh. A.10 - Prob. 31AYUCh. A.10 - Prob. 32AYUCh. A.10 - Prob. 33AYUCh. A.10 - Prob. 34AYUCh. A.10 - Prob. 35AYUCh. A.10 - Prob. 36AYUCh. A.10 - Prob. 37AYUCh. A.10 - Prob. 38AYUCh. A.10 - Prob. 39AYUCh. A.10 - Prob. 40AYUCh. A.10 - Prob. 41AYUCh. A.10 - Prob. 42AYUCh. A.10 - Prob. 43AYUCh. A.10 - Prob. 44AYUCh. A.10 - Prob. 45AYUCh. A.10 - Prob. 46AYUCh. A.10 - Prob. 47AYUCh. A.10 - Prob. 48AYUCh. A.10 - Prob. 49AYUCh. A.10 - Prob. 50AYUCh. A.10 - Prob. 51AYUCh. A.10 - Prob. 52AYUCh. A.10 - Prob. 53AYUCh. A.10 - Prob. 54AYUCh. A.10 - Prob. 55AYUCh. A.10 - Prob. 56AYUCh. A.10 - Prob. 57AYUCh. A.10 - Prob. 58AYUCh. A.10 - Prob. 59AYUCh. A.10 - Prob. 60AYUCh. A.10 - Prob. 61AYUCh. A.10 - Prob. 62AYUCh. A.10 - Prob. 63AYUCh. A.10 - Prob. 64AYUCh. A.10 - Prob. 65AYUCh. A.10 - Prob. 66AYUCh. A.10 - Prob. 67AYUCh. A.10 - Prob. 68AYUCh. A.10 - Prob. 69AYUCh. A.10 - Prob. 70AYUCh. A.10 - Prob. 71AYUCh. A.10 - Prob. 72AYUCh. A.10 - Prob. 73AYUCh. A.10 - Prob. 74AYUCh. A.10 - Prob. 75AYUCh. A.10 - Prob. 76AYUCh. A.10 - Prob. 77AYUCh. A.10 - Prob. 78AYUCh. A.10 - Prob. 79AYUCh. A.10 - Prob. 80AYUCh. A.10 - Prob. 81AYUCh. A.10 - Prob. 82AYUCh. A.10 - Prob. 83AYUCh. A.10 - Prob. 84AYUCh. A.10 - Prob. 85AYUCh. A.10 - Prob. 86AYUCh. A.10 - Prob. 87AYUCh. A.10 - Prob. 88AYUCh. A.10 - Prob. 89AYUCh. A.10 - Prob. 90AYUCh. A.10 - Prob. 91AYUCh. A.10 - Prob. 92AYUCh. A.10 - Prob. 93AYUCh. A.10 - Prob. 94AYUCh. A.10 - Prob. 95AYUCh. A.10 - Prob. 96AYUCh. A.10 - Prob. 97AYUCh. A.10 - Prob. 98AYUCh. A.10 - Prob. 99AYUCh. A.10 - Prob. 100AYUCh. A.10 - Prob. 101AYUCh. A.10 - Prob. 102AYUCh. A.10 - Prob. 103AYUCh. A.10 - Prob. 104AYUCh. A.10 - Prob. 105AYUCh. A.10 - Prob. 106AYUCh. A.10 - Prob. 107AYUCh. A.10 - Prob. 108AYUCh. A.10 - Prob. 109AYUCh. A.10 - Prob. 110AYUCh. A.10 - Prob. 111AYUCh. A.10 - Prob. 112AYUCh. A.10 - Prob. 113AYUCh. A.10 - Prob. 114AYUCh. A.10 - Prob. 115AYUCh. A.10 - Prob. 116AYUCh. A.10 - Prob. 117AYU

Additional Math Textbook Solutions

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If f(x)={2x+4if3x1x31if1x5 find : f(2) (b) f(0) (c) f(1) (d) f(3)

Precalculus

To find the estimated and actual value of the product 335⋅425 .

Glencoe Math Accelerated, Student Edition

Evaluate for the vector field along the curve from (4, 2) to (1, –1).

University Calculus: Early Transcendentals (4th Edition)

The derivative of f(x) , f′(x) and f"(x) .

Calculus: Early Transcendentals (3rd Edition)

Continuity at a point Determine whether the following functions are continuous at a. Use the continuity checkli...

Calculus: Early Transcendentals (2nd Edition)

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Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book

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