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Nature of Roots

the value of ...

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the value of a for which the equation (1-a^2)x^2 + 2ax -1 =0 has roots belonging to (0,1) is

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Q. The value of

a

for which the equation

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

has roots belonging to

(0, 1)

Q. The necessary and sufficient condition for the equation

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

to have roots lying in the interval

(0, 1)

Q. Find the value of

a

for which both the roots of the equation

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

0

1

Both roots of $(a^{2} - 1) x^{2} + 2 a x + 1 = 0$ belong to the interval (0,1) then exhaustive set of values of 'a' is :

Q. Show that there is no real number K belonging to [0,1] for which the equation

x^{2} - 3 x + k = 0

has two imaginary roots .

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