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Monotonically Decreasing Functions

THE RANGE OF ...

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THE RANGE OF VALUES OF a so that all the roots of the euation 2x^3-3x^2-12x+a=0 are real and distinct

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Q. The range of values of

α

so that all the roots of the equation

2 x^{3} - 3 x^{2} - 12 x + α = 0

are real distinct belongs to

Q. If the equation

2 x^{3} + 3 x^{2} - 12 x + d = 0

has 3 real and distinct roots, then

d

Q. Find the range of values of the parameter

a

x^{3} - 3 x + a = 0

has three real and distinct roots.

Q. The sum of all possible value(s) of

a

so that the equation

(x^{2} + 2 a x + 2 a + 3) (x^{2} + 2 a x + 4 a + 5) = 0

has exactly three real and distinct roots is

Q. Number of intergers in the range of 'a' so that the equation

x^{3} - 3 x + a = 0

has all its roots real and distinct,is

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