If roots of equation $x^{2} - 2 m x + m^{2} - 1 = 0$ lie in the interval $(- 2, 4)$ , then find m

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Solution

Given,

$x^{2} - 2 m x + m^{2} - 1 = 0$

$(x - m)^{2} - 1 = 0$

$(x - m + 1) (x - m - 1) = 0$

$x = m - 1, m + 1 - 2 < m - 1, m + 1 < 4$

$m > - 1, m < 3$

$∴ - 1 < m < 3$

the value of m ranges between -1 and 3.

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Similar questions

x^{2} - 2 m x + m^{2}

if the roots of the equation x² -2mx +m² - 1 =0 lie in the interval (-2,4) then,

a) m ~ (-1,3) b) m~(1,5)

c) m~(-3,1) d) m~(-1.5)

where ~ stand for "belongs to".

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x^{2} - 2 m x + m^{2} - 1 = 0

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x^{2} - 2 m x + m^{2} + 1 = 0

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