Let a, b and c be positive real numbers. If x^2-b x a x-c = m-1 m+1 has two roots which are numerically equal but opposite in sign, then the value of m is

Step-by-step solution

aligned & Given, x^2-b x a x-c = m-1 m+1 & (x^2-b x )(m+1)=(m-1)(a x-c) & x^2(m+1)-x(b(m+1)+a(m-1)+c(m-1)=0 aligned Let p and -p are roots of Eq. (i), then aligned & Sum of roots p+(-p)= b(m+1)+a(m-1) m+1 & 0= (b+a) m+(b-a) m+1 & m(b+a)+(b-a)=0 & m= a-b a+b aligned