JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Easy

1 of 1

Analyzing +4 | -1

The real number

k

for which the equation,

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

has two distinct real roots in [0, 1]

View answer and explanation

Correct option: D

does not exist

Option D (does not exist) is correct because the derivative of the function is always positive, meaning the function is strictly increasing and can have at most one real root.

More Questions from THEORY OF EQUATION

Practice All Chapter MCQs →

The maximum number of real roots of the equation

{x^{2n}} - 1 = 0

is The number of roots of the equation

\frac{1}{x}+\frac{1}{\sqrt{\left(1-x^2\right)}}=\frac{35}{12}

is How many real solutions does the equation

x^7+14 x^5+16 x^3+30 x-560=0

have? If

x_1, x_2, x_3, \ldots, x_n

are the roots of the equation

x^n+a x+b=0

, the value of

\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_1-x_4\right) \ldots\left(x_1-x_n\right)

is The polynomials

P(x)=k x^3+3 x^2-3

and

Q(x)=2 x^3-5 x+k

, when divided by

(x-4)

leave the same remainder, then

k

is equal to: If

{\left( {x - 1} \right)^3}

is a factor of

{x^4} + a{x^3} + b{x^2} + cx - 1,

then the other factor is