For what interval of m do all roots of the qu | vedclass

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(A) The given quadratic equation is $x^2 - 2mx + m^2 - 1 = 0$.This can be rewritten as $(x - m)^2 = 1$.Taking the square root on both sides,we get $x

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$-1 < m < 3$

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(A) The given quadratic equation is $x^2 - 2mx + m^2 - 1 = 0$.This can be rewritten as $(x - m)^2 = 1$.Taking the square root on both sides,we get $x - m = \pm 1$,which implies $x = m + 1$ or $x = m - 1$.For the roots to lie between $-2$ and $4$,both roots must satisfy the inequality $-2 For $x = m + 1$: $-2 For $x = m - 1$: $-2 To satisfy both conditions simultaneously,we take the intersection of the intervals $(-3, 3)$ and $(-1, 5)$,which is $(-1, 3)$.

Quadratic expression	The minimum value
i) $x^2 + 4x + 6$	a) $1$
ii) $x^2 - 2x + 5$	b) $2$
iii) $x^2 + 6x + 18$	c) $4$
iv) $x^2 - 4x + 5$	d) $9$

For what interval of $m$ do all roots of the quadratic equation $x^2 - 2mx + m^2 - 1 = 0$ lie between $-2$ and $4$?

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