Question
If the roots of a(b−c)x2+b(c−a)x+c(a−b) = 0 be equal then a,b,c are in
Answer: Option C
:
C
Since the roots of the quadratic equation in x are equal, we have (B2−4AC) = 0
⇒b2(c−a)2−4ac(b−c)(a−b) = 0
⇒b2(c2−2ca+a2)−4ac(ba−b2−ca+bc) = 0
⇒b2(c2+2ca+a2)−4ac{b(a+c)−ac}= 0
⇒b2(a+c)2−4ac{b(a+c)−ac}= 0
Which can be seen to be true, if
b = 2aca+c or b(a+c) = 2ac i.e., if a,b,c are in H.P.
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:
C
Since the roots of the quadratic equation in x are equal, we have (B2−4AC) = 0
⇒b2(c−a)2−4ac(b−c)(a−b) = 0
⇒b2(c2−2ca+a2)−4ac(ba−b2−ca+bc) = 0
⇒b2(c2+2ca+a2)−4ac{b(a+c)−ac}= 0
⇒b2(a+c)2−4ac{b(a+c)−ac}= 0
Which can be seen to be true, if
b = 2aca+c or b(a+c) = 2ac i.e., if a,b,c are in H.P.
Was this answer helpful ?
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