JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

If the functions

f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}

and

g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b

have a common extreme point, then

a+2 b+7

is equal to

View answer and explanation

Correct option: C

The correct answer is 6 because the common extreme point implies that the derivatives of the two functions have a common root, which allows us to solve for a + 2b + 7.

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The maximum number of real roots of the equation

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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