JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Application +4 | -1

If 1, 2, 3 and 4 are the roots of the equation

{x^4} + a{x^3} + b{x^2} + cx + d = 0

, then

a + 2b + c

is equal to

View answer and explanation

Correct option: C

Option A (10) is correct because by expanding the polynomial with roots 1, 2, 3, and 4, and comparing coefficients, we can find the values of a, b, and c, and then calculate a + 2b + c = 10.

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The maximum number of real 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

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x_1, x_2, x_3, \ldots, x_n

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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

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is equal to: If

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

is a factor of

{x^4} + a{x^3} + b{x^2} + cx - 1,

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