Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Videos

Question

Chapter 7.7, Problem 1WE

To determine

Find the solution for the equation x2−3x+6=0 and check answer by using the theorem about the sum and product of the root.

Expert Solution & Answer

Answer to Problem 1WE

The solution for the quadratic equation is (x) equal to {3+15i2,3−15i2} .

Explanation of Solution

Given information: The given equation is,

x2−3x+6=0 ....(1)

Calculation: With the help of quadratic formula the equal (1) is solved as,

x=−(−3)±(−3)2−4(1)(6)2(1) ....(Quadratic formula fora=1,b=−3,c=6)=3±−152=3±15i2=3+15i2,3−15i2

Hence the solution for the quadratic equation is (x) equal to {3+15i2,3−15i2} .

Now with the help of theorem for sum and product of roots of quadratic equation, the sum (S) and product (P) of roots is evaluated as,

Sum of roots=3+15i2+3−15i2=3Product of roots=(3+15i2)(3−15i2)=9−15i24=9−15(−1)4 ....(i2=−1)=6

Again from (1) apply theorem property for sum and product of roots gives,

Sum of roots=−(−3)(1)....(a=1,b=−3and c=6)=3Product of roots=(6)(1).... (a=1,b=−3and c=6)=6

Hence, verified that the equation x2−3x+6=0 has sum of roots 3 and product of roots 6.

Chapter 7.7, Problem 15OE

Chapter 7.7, Problem 2WE

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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Find the solution for the equation x 2 − 3 x + 6 = 0 and check answer by using the theorem about the sum and product of the root.

Concept explainers

Videos

Find the solution for the equation x2−3x+6=0 and check answer by using the theorem about the sum and product of the root.

Answer to Problem 1WE

Explanation of Solution

Chapter 7 Solutions

Additional Math Textbook Solutions