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If $I, m, n$ are real and $I \neq m$, then the roots of the equation $(I-m) x^2-5(I+m) x-2(I-m)=0$ are
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Real and distinct
Given equation is $(I-m) x^2-5(I+m) x-2(I-m)=0$
Its discriminant $D=25(I+m)^2+8(I-m)^2$
which is positive, since $I, m, n$ are real and $I \neq m$ Hence roots are real and distinct.
Its discriminant $D=25(I+m)^2+8(I-m)^2$
which is positive, since $I, m, n$ are real and $I \neq m$ Hence roots are real and distinct.
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