a. Explanation Given information: The quadratic equation is x 2 − 6 x + 11 = 0 . Proof: if 3 + i 2 is a root of x 2 − 6 x + 11 = 0 then after substitute the root in the equation, it satisfy the equation, x 2 − 6 x + 11 = 0 ( 3 + i 2 ) 2 − 6 ( 3 + i 2 ) + 11 = 0 [substitute] 9 + 2 i 2 + 6 2 i − 18 − 6 2 i + 11 = 0 [expand square and multiply] 9 − 2 − 18 + 11 = 0 [ i 2 = − 1 and cancel out common] 0 = 0 [simplify] b. To determine To find: the another root. Answer The another root is 3 − i 2 . Explanation Given information: The quadratic equation is x 2 − 6 x + 11 = 0 . Calculation: it is known that if a quadratic equation has a imaginary root then the conjugate of imaginary root must be a root of that quadratic equation. Thus, the another root of quadratic equation is 3 − i 2 .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 7.7, Problem 37WE

To determine

Toshow: that 3+i2 is a root of x2−6x+11=0 .

Expert Solution

Explanation of Solution

Given information:

The quadratic equation is x2−6x+11=0 .

Proof: if 3+i2 is a root of x2−6x+11=0 then after substitute the root in the equation, it satisfy the equation,

x2−6x+11=0(3+i2)2−6(3+i2)+11=0 [substitute]9+2i2+62i−18−62i+11=0 [expand square and multiply]9−2−18+11=0 [i2=−1 and cancel out common]0=0 [simplify]

To determine

To find: the another root.

Expert Solution

Answer to Problem 37WE

The another root is 3−i2 .

Explanation of Solution

Given information:

The quadratic equation is x2−6x+11=0 .

Calculation:it is known that if a quadratic equation has a imaginary root then the conjugate of imaginary root must be a root of that quadratic equation.

Thus, the another root of quadratic equation is 3−i2 .

Chapter 7.7, Problem 36WE

Chapter 7.7, Problem 38WE

Chapter 7 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 7.1 - Prob. 1OE Ch. 7.1 - Prob. 2OE Ch. 7.1 - Prob. 3OE Ch. 7.1 - Prob. 4OE Ch. 7.1 - Prob. 5OE Ch. 7.1 - Prob. 6OE Ch. 7.1 - Prob. 7OE Ch. 7.1 - Prob. 8OE Ch. 7.1 - Prob. 9OE Ch. 7.1 - Prob. 10OE

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