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If the roots of equation (x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0 are equal, then
- a)a+b+c=0
- b)a=b=c
- c)a−b+c=0
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the roots of equation (x−b)(x−c)+(x−c)(x−a)...
Given the equation
(x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0
⇒3x2−2(a+b+c)x+(ab+bc+ca)=0
Since, roots of the equation are equal, then discriminant D=0
⇒[−2(a+b+c)]2−4×3×(ab+bc+ca)=0
⇒4(a+b+c)2−12(ab+bc+ca)=0
⇒(a+b+c)2−3(ab+bc+ca)=0
⇒[a2+b2+c2+2(ab+bc+ca)]−3(ab+bc+ca)=0
⇒a2+b2+c2−(ab+bc+ca)=0
⇒2a2+2b2+2c2−2(ab+bc+ca)=0
⇒(a−b)2+(b−c)2+(c−a)2=0
This is only possible when a=b=c
(x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0
⇒3x2−2(a+b+c)x+(ab+bc+ca)=0
Since, roots of the equation are equal, then discriminant D=0
⇒[−2(a+b+c)]2−4×3×(ab+bc+ca)=0
⇒4(a+b+c)2−12(ab+bc+ca)=0
⇒(a+b+c)2−3(ab+bc+ca)=0
⇒[a2+b2+c2+2(ab+bc+ca)]−3(ab+bc+ca)=0
⇒a2+b2+c2−(ab+bc+ca)=0
⇒2a2+2b2+2c2−2(ab+bc+ca)=0
⇒(a−b)2+(b−c)2+(c−a)2=0
This is only possible when a=b=c
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If the roots of equation (x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0are equal, thena)a+b+c=0b)a=b=cc)a−b+c=0d)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
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If the roots of equation (x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0are equal, thena)a+b+c=0b)a=b=cc)a−b+c=0d)None of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the roots of equation (x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0are equal, thena)a+b+c=0b)a=b=cc)a−b+c=0d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of equation (x−b)(x−c)+(x−c)(x−a)+(x−a)(x−b)=0are equal, thena)a+b+c=0b)a=b=cc)a−b+c=0d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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