JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

If the two roots of the equation,

(a-1)\left(x^{4}+x^{2}+1\right)+

(a+1)\left(x^{2}+x+1\right)^{2}=0

are real and distinct, then the set of all values of '

a

' is :

View answer and explanation

Correct option: B

\left(-\frac{1}{2}, 0\right) \cup\left(0, \frac{1}{2}\right)

Option B (

\left(-\frac{1}{2}, 0\right) \cup\left(0, \frac{1}{2}\right)

) is correct because by simplifying the given equation and analyzing the discriminant of the resulting quadratic, we can find the range of values for 'a' that satisfy the condition of having real and distinct roots.

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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