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  4. The number of integral values of m, for which the roots of x2-2 m x+m2-1=0 will lie between -2 and 4 is -

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Q. The number of integral values of $m$, for which the roots of $x^2-2 m x+m^2-1=0$ will lie between $-2$ and 4 is -

Complex Numbers and Quadratic Equations

Solution:

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Hint : $x^2-2 m x+m^2-1=0$
(i) $ f (-2)>0$
(ii) $ f (4)>0$
(iii) $D \geq 0$
(iv) $-2<\frac{-b}{2 a}<4$
Common solution $m \in(-1,3)$