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Quadratic Formula

If the roots ...

Question

If the roots of $x^{2} - 2 m x + m^{2} - 1 = 0$ lie between -2 and 4, then

- 3 \leq m \leq 4

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- 3 \leq m \leq 5

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- 1 \leq m \leq 5

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- 1 \leq m \leq 3

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Solution

The correct option is D $- 1 \leq m \leq 3$
The roots of the equation, $x^{2} - 2 m x + m^{2} - 1 = 0$ are:

$\frac{2 m \pm \sqrt{4 m^{2} - 4 (m^{2} - 1)}}{2}$
= $m \pm 1$
They lie between -2 and 4
hence, $m - 1 \geq - 2$ and $m + 1 \leq 4$
$m \geq - 1$ and $m \leq 3$
$- 1 \leq m \leq 3$

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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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