JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

If for a positive integer

n

, the quadratic equation 

x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + ...... + \left( {x + n - 1} \right)\left( {x + n} \right) = 10n

has two consecutive integral solutions, then

n

is equal to

View answer and explanation

Correct option: A

Option A (11) is correct because it is the value of n that satisfies the given conditions for the quadratic equation to have two consecutive integral solutions.

More Questions from THEORY OF EQUATION

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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