Question:
If a,b,c are real numbers then the roots of
(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
If a,b,c are real numbers then the roots of
(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
Show Hint
Check discriminant to decide nature of roots.
Updated On: Mar 20, 2026
- real
- imaginary
- positive
- negative
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The Correct Option is A
Solution and Explanation
Step 1: Simplify equation: 3x²-2(a+b+c)x+(ab+bc+ca)=0
Step 2: Discriminant: Δ=[2(a+b+c)]²-12(ab+bc+ca)\ge0
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