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 ___________.

Select an option to instantly check whether it is correct or wrong.

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The area of the region enclosed by the parabolas y=4x-x^2 and 3y=(x-4)^2 is equal to

Area of the region (x,y):x^2+(y-2)^2≤4,x^2≥2y is

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

Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

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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