Question

the equation x^2 +bx+c=0 has distinct roots. if 2 is subtracted from each root. answer is the reciprocal of the orginal roots. value of b^2 +c

Answer 1

let the roots be a and b.

now subtracting 2 from each root ..

a-2 &b-2 r equal to reciprocal of original roots i.e a&b .

so,a-2=1/a &b-2=1/2

solving we get a=& b=1±√2

so we take a=1+√2 & b=1-√2

so

b^2+c^2+bc=(a+b)2 +ab2 +(a+b)*ab=4+1-2=3

hence the answer is 3

Hope this will help u.....