Let a be an integer such that all the real roots of the polynomial 2x 5 + 5x 4 + 10x 3 + 10x 2 + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equa...

Let, f(x) = 2x^5 + 5x^4 + 10x^3 + 10x^2 + 10x + 10 f'(x) = 10(x^4 + 2x^3 + 3x^2 + 2x + 1) = 10( x^2 + 1 x^2 + 2( x + 1 x ) + 3 ) = 10( ( x + 1 x )^2 + 2( x + 1 x ) + 1 ) = 10( ( x + 1 x ) + 1 )^2 > 0; x R is strictly increasing function. Since, it is an odd degree polynomial it will have exactly ...

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Let a be an integer such that all the real roots of the poly: null (Mathematics) | DivineJEE

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Mathematics

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Mathematics

Let a be an integer such that all the real roots of the polynomial
2x⁵ + 5x⁴ + 10x³ + 10x² + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equal to ___________.

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For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

Let Z be the set of integers. If A = { x in Z:2^{(x + 2) ( x^{2} - 5x + 6 )} = 1 } and = { x in Z : - 3 < 2x - 1 < 9}, then the . number of subsets of the set A X B is

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The area enclosed by the curves xy+4y=16 and x+y=6 is equal to :

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For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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