If f(x) is a quadratic expression s...
Question
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If f(x) is a quadratic expression such that f(1)+f(2)=0, and -1 is a root of f(x) = 0,  

then the other root of f(x) =0 is

 

(A) -5/8

(B) -8/5

(C) 5/8

(D) 8/5

 

JEE/Engineering Exams
Maths
Solution
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If f(x) is a quadratic expression such that f(1)+f(2)=0, and -1 is a root of f(x) = 0,    then the other root of f(x) =0 is
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let f(x)= ax2+bx+c =0 given f(1)+f(2) =0       &  f(-1)=0 (a+b+c) + 3a +2b +c =0       a(-1)2-b+c=0 = 5a +3b +2c =0                  a-b+c=0 using (1) & 11×43 5a+3b+2C=0 3a-3b+3c=0           8a+ 5c=0 we know αβ =4a as α=-1  β=-ca=85  (d)

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