JEE Main 2013 (Offline) | Quadratic Equation and Inequalities Question 112 | Mathematics

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \right]$$

lies between 1 and 2

lies between 2 and 3

lies between $$ - 1$$ and 0

does not exist.

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

If the equations $${x^2} + 2x + 3 = 0$$ and $$a{x^2} + bx + c = 0,$$ $$a,\,b,\,c\, \in \,R,$$ have a common root, then $$a\,:b\,:c\,$$ is

$$1:2:3$$

$$3:2:1$$

$$1:3:2$$

$$3:1:2$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

The equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has:

infinite number of real roots

no real roots

exactly one real root

exactly four real roots

AIEEE 2010

MCQ (Single Correct Answer)

-1

If $$\alpha $$ and $$\beta $$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2009}} = $$

$$\, - 1$$

$$\, 1$$

$$\, 2$$

$$\, - 2$$

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