PRECALCULUS:...COMMON CORE ED.-W/ACCESS
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
10th Edition
ISBN: 9780134781839
Author: Demana
Publisher: PEARSON
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Expert Solution & Answer
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Chapter P.6, Problem 49E
Solution

The solution of the equation ax2+bx+c=0 where a,b,c are real numbers.

(A) 2+3i

Given:

The equation, ax2+bx+c=0

One solution is given, 2−3i

Concept used:

  • Product of powers property, an⋅am=an+m
  • FOIL to multiply binomials, a+bc+d=a⋅c+a⋅d+b⋅c+b⋅d
  • Properties of complex number: −1=i, i2=−1, i3=−i
  • The complex conjugate of a+bi is a−bi .
  • Difference of squares formula, a+ba−b=a2−b2

Calculation:

In order to find the other solution of the equation ax2+bx+c=0 , the other solution is 2+3i because the complex solutions of a quadratic equation with real coefficient always occur in complex conjugate.

If a+bi is a solution, then a−bi will also have a solution.

So, the solution is 2−3i , 2+3i .

Thus, option (A) is the correct answer.

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Chapter P.6, Problem 48E
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Chapter P.6, Problem 50E

Chapter P Solutions

PRECALCULUS:...COMMON CORE ED.-W/ACCESS

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