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Both the roots of the equation (x-b)(x-c...

Both the roots of the equation `(x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0` are always a. positive b. real c. negative d. none of these

A

non-real complex

B

real and equal

C

integers

D

real and disinct

Text Solution

Verified by Experts

Given that ` a lt b lt c lt d ` . Let
` f(x) = (x - a) (x - c) + 2(x - b) (x - d)`
`rArr f(b) = (b - a) (b - c) lt 0 `
and ` f(d) = (d - a) (d - c) (d - c) gt 0 `
Hence , f(x) = 0 has one root in (b, d) , Also `f(a) f(c) lt 0 `. So the
other root lies in (a,c) . Hence, roots of the equation are real
and disinct .
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