Find the values of 't' in the equation $x^{2}$ - 2tx + $t^{2}$ - 1 = 0 such that exactly one root lies in between the numbers 2 and 4, and no root of the equation is either 2 (or) 4.

Q. If

a \in R

and the roots of

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

lies between the roots of

x^{2} - 2 (a + 1) x + a (a - 1) = 0

, then

a

belongs to

Q. If the smaller root of the equation

x^{2} - a x + 4 = 0

lies between

- 1

and

- 2

, then belongs to

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One root of x3+x2−2x−1=0 lies between

The correct options are A −1 and 0 B −2 and −1x3+x2−2x−1=0f(0)=−1f(−1)=1f(−2)=−1f(−3)=−13f(−4)=−71As f(−1)>0 and f(−2)<0Therefore one roots lies between −2 and −1

One root of $x^{3} + x^{2} - 2 x - 1 = 0$ lies between

The correct options are
A $- 1$ and $0$
B $- 2$ and $- 1$
$x^{3} + x^{2} - 2 x - 1 = 0$
$f (0) = - 1 f (- 1) = 1 f (- 2) = - 1 f (- 3) = - 13 f (- 4) = - 71$
As $f (- 1) > 0$ and $f (- 2) < 0$
Therefore one roots lies between $- 2$ and $- 1$