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Properties of Determinants

find the real...

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find the real values of the parameter a such that (2a +1)x^2 - a(x-1)=2 has one root greater than 1 and other less than 1

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Similar questions

Q. Let the equation

x^{2}

+ 2(a - 1)x + a + 5 = 0, where 'a' is a parameter, match the real value of 'a' so that the given equation has :-

Column - I	Column - II
(A) Imaginary roots	(P) $(- \infty, - \frac{8}{7})$
(B) One root less than 3 other root is greater than 3	(Q) (-1, 4)
(C) One root less than 1 & other root is greater than 3	(R) $(- \infty, - \frac{4}{3})$

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

has one root less than

a

and other root greater than

a

, then which of the following is true

Q. The value of

a

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

may have one root less than

a

and other root greater than

a

Q. The set of values of

a

for which one root of the equation

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

is greater than

1

and the other root is less than zero is

Q. Find the value of

m

such that one root is greater than

2

and the other root is smaller than

1

of the quadratic equation

x^{2} - (m - 3) x + m = 0

(m \in R)

.

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