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4. A sketch of r(x) is shown. Which of the following could be an equation for r(x)? a. r(x) = (x-a) (x + b) (x + c) b. r(x) = (x + a)(x-b)(x-c) c. r(x) = (x + a)(x-b)(x-c)² d. r(x) = (x-a) (x + b) (x + c)² Aj -b

4. A sketch of r(x) is shown. Which of the following could be an equation for r(x)? a. r(x) = (x-a) (x + b) (x + c) b. r(x) = (x + a)(x-b)(x-c) c. r(x) = (x + a)(x-b)(x-c)² d. r(x) = (x-a) (x + b) (x + c)² Aj -b

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. A sketch of r(x) is shown. Which of the following could be an equation for r(x)? a. r(x) = (x-a) (x + b) (x + c) b. r(x) = (x + a)(x-b)(x-c) c. r(x) = (x + a)(x-b)(x-c)² d. r(x) = (x-a) (x + b) (x + c)² W 10
Transcribed Image Text:4. A sketch of r(x) is shown. Which of the following could be an equation for r(x)? a. r(x) = (x-a) (x + b) (x + c) b. r(x) = (x + a)(x-b)(x-c) c. r(x) = (x + a)(x-b)(x-c)² d. r(x) = (x-a) (x + b) (x + c)² W 10
Expert Solution
Step 1

The given graph of r(x) has zeros at point a , -b and  -c .

For the zeros of r(x) , put  r(x)=0 .

(a).    r(x) = (x-a)(x+b)(x+c)

⇒   r(x) = 0

⇒  (x-a)(x+b)(x+c)=0⇒    x = a , -b , -c

(b).      r(x)= (x+a)(x-b)(x-c)

⇒  r(x) = 0

⇒    (x+a)(x-b)(x-c) = 0⇒        x= -a , b , c

=> Zeros of  r(x)=(x+a)(x-b)(x-c) and r(x) = (x+a)(x-b)(x-c)2  are  -a , b , c .

=>  Option  (b)  and  (c) are not possible .

But zeros of r(x)=x-ax+bx+c and r(x)=x-ax+bx+c2 are  a , -b , -c.

=> Either ption  (a) or option (d) is possible .

We do further investigation .

 

 

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