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Rolle's Theorem

Let the sets ...

Question

Let the sets be A = {x : x is a real root of equation (x2 – 5x + 6)·(x2 – 12x + 35) = 0} and B = {1, 2, 3, 4, 5}, then the number of ordered pairs in (A × B) ∩ (B × A) is

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A = {x \in R : x^{2} - | x | - 2 = 0}

B = {α + β, α β}

α, β

x^{2} + | x | - 2 = 0 .

(a, b) \in A \times B,

a, b

A = {x | x is an integer root of the equation x^{5} - 6 x^{4} + 11 x^{3} - 6 x^{2} = 0}

B = {x | x is a real root of the equation a x^{5} + 2 a x^{3} + 2 b x^{2} + b = 0, a, b \in R such that the given equation have maximum number of real roots.}

f (x) = \sqrt{\frac{x^{2} + a x + 4}{x^{2} + b x + 16}}

x

(a, b)

a, b \in I

(a, b)

α

x^{2} + a x + b = 0, α^{2} - 2

x_{1}

x_{2}

x^{2} - 3 x + A = 0

x_{3}

x_{4}

x^{2} - 12 x + B = 0

x_{1}, x_{2}, x_{3}, x_{4}

\frac{B}{2 A}

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