JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Hard

1 of 1

Analyzing +4 | -1

The number of real roots of the equation

1 + {a_1}x + {a_2}{x^2} + \ldots + {a_n}{x^n} = 0,

where

\left| x \right| < \frac{1}{3}\;\mathrm{and\;}\left| {{a_n}} \right| < 2,

View answer and explanation

Correct option: C

0 for any

n \in N

Option C (0 for any

n \in N

) is correct because the given equation has no real roots for any n, as the expression is always positive within the specified range.

More Questions from THEORY OF EQUATION

Practice All Chapter MCQs →

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

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

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

x_1, x_2, x_3, \ldots, x_n

x^n+a x+b=0

\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)

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

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

(x-4)

k

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

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