JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Easy

1 of 1

Application +4 | -1

a

and

b

are real numbers such that

{\left( {2 + \alpha } \right)^4} = a + b\alpha ,

where

\alpha = \frac{{ - 1 + i\sqrt 3 }}{2},

then

a + b

is equal to

View answer and explanation

Correct option: C

The correct answer is C (9) because it is the sum of a and b, where a and b are real numbers satisfying the given equation involving a complex number alpha.

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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

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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

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and

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

, when divided by

(x-4)

leave the same remainder, then

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is equal to: If

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

is a factor of

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