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for x being real when the expression (x-a)(x-b)/(x-c) assumes real values ques of iit 1994 please give deyailed solution

for x being real when the expression (x-a)(x-b)/(x-c) assumes real values


ques of iit 1994


please give deyailed solution

Grade:12th Pass

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

(x-a)(x-b)/(x-c) =k(real), x2-(a+b)x+ab=kx-kc, x2-(a+b+k)x+ab+kc=0,if x is real, discriminant≥0,(a+b+k)^2≥4(ab+kc)

k2+(a+b)2+2k(a+b)≥4(ab+kc), k2+2k(a+b-2c)+(a-b)^2≥0,k≤-(a+b-2c)-√((a+b-2c)2-(a-b)2)

or k≥-(a+b-2c)+√((a+b-2c)2-(a-b)2)

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