For what positive values of m the equation (1+m)x2−2(1+3m)x+(1+8m)=0 has equal roots.
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Solution
Given equation is (1+m)x2−2(1+3m)x+(1+8m)=0 ...(i) Let D be the discriminant of equation (i). Roots of equation (i) will be equal if D=0. or 4(1+3m)2−4(1+m)(1+8m)=0 or 4(1+9m2+6m−1−9m−8m2)=0 or m2−3m=0 or, m(m−3)=0 ∴m=0,3.