JEE MATHEMATICS MCQ: THEORY OF EQUATION

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Analyzing +4 | -1

If roots of the equation

{x^4} - 8{x^3} + b{x^2} + cx + 16 = 0

are positive then

View answer and explanation

Correct option: C

b = 24,c = - 32

Option D (

b = 24, c = -32

) is incorrect. The correct answer is D (

b = 24, c = 32

) because the roots are equal, allowing us to expand (x-2)⁴ and match coefficients.

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{x^{2n}} - 1 = 0

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x^7+14 x^5+16 x^3+30 x-560=0

x_1, x_2, x_3, \ldots, x_n

x^n+a x+b=0

\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)

P(x)=k x^3+3 x^2-3

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

(x-4)

k

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

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