JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Application +4 | -1

\mathrm{P}(\mathrm{x})

be a polynomial of degree 4 , with

\mathrm{p}(2)=-1, \mathrm{p}^{\prime}(2)=0, \mathrm{p}^{\prime \prime}(2)=2, \mathrm{p}^{\prime \prime \prime}(2)=-12

and

p^{\prime \prime \prime}(2)=24

then

p^{\prime \prime}(1)

is equal to:

View answer and explanation

Correct option: C

Option C (26) is correct because after finding the polynomial's coefficients using the given derivatives and value at x=2, the second derivative at x=1 is calculated to be 26.

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The maximum number of real roots of the equation

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\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