If `f(x)=(x-a)(x-b),` then show that `f(x) >= -((a-b)^2)/4.` Find the least integral value of 'k' for which the quadratic polynomial

If f(x) =(x-a) (x-b) , then show that f(x) ge (a-b)^(2)/4

Find the least integral value of 'k' for which the quadratic polynomial (k-1)x^(2) + 8x + k + 5 gt 0 AA x in R

Find the least value of f(x)=ax+(b)/(x) where a>0,quad b>0 and x>0

If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is

If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is

Range of function f(x) = cos (k sin x) is [-1, 1], then the least positive integral value of k will be

Consider the quadratic polynomial f(x)=x^(2)-4ax+5a^(2)-6a a) Find the smalest positive integral value of a for which f(x) positive integry real x.(i) Find the largest distance between the roots of equation f(x)=0.

Range ofthe function f(x)=cos(K sin x) is [-1,1], then the least positive integral value of K will be

If x=0 and x=-1 are the roots of the polynomial f(x)=2x^(3)-3x^(2)+ax+b, find the value of a and b