For every `x in R` the polynomail `x^8-x^5+x^2-x+1` is

If the remainder obtained on dividing the polynomial 2x^(3)-9x^(2)+8x+15 by (x-1) is R_(1) and the remainder obtained on dividing the polynomial x^(2)-10x+50 by (x-5) is R_(2), then what is the value of R1-R2?

If the function f(x)=(sqrt(x^(2)+kx+1))/(x^(2)-k) is continuous for every x in R , then possible integral values of k

For x in R , the maximum value of sqrt(x^4 - 5x^2 – 8x + 25) - sqrt( x^4 – 19x^2 + 100) is

If f(x) = frac {x^2 -1}{x^2 +1} , for every real x, then the minimum value of f(x) is.

For x in R , the least value of (x^(2)-6x+5)/(x^(2)+2x+1) is

If f(x) = x^(3) + (a – 1) x^(2) + 2x + 1 is strictly monotonically increasing for every x in R then find the range of values of ‘a’

If r_(1), is the remainder when 3x^(4)-8x+5x^(2)-7x-13 is divided by x+k and r_(1), is when 9x^(3)-4x^(2)-3x+8 is divided by x-(k)/(2) and quad if quad (3)/(8)r_(1)-kr_(2)=(1)/(8), find the remainder when 32x^(3)+27x^(2)-43x+100 is divided by x-k.

For every value of x the function f(x)=1/(5^(x)) is

If a sin^(2) x +b lies in the interval [-2,8] for every x in R then find the value of (a-b)