`" Number of zeros of the cubic "f(x)=x^(3)+2x+k AA k in R" ,is "`

If the product of zeros of the quadratic polynomial f(x)=x^(2)-4x+k is 3, find the value of k.

If the sum of the squares of zeroes of the quadratic polynomial f(x) = x^(2) - 8x + k is 40, find the value of k.

Given that the zeros of the cubic polynomial f(x) = x^3 -6 x^2 + 3x + 10 are a, a+b, a + 2b for some real number a and b. Find the values of a and b as well as the zeros of the given polynomial.

If the zeros of the polynomial f(x)=x^(3)-12x^(2)+39x+k are in A.P.find the value of k.

Suppose a in R . Define f and g as follows: f(x) =(a^(2) - 4a + 3)x^(2) + (a^(2) -1)a AA x in R and g(x) = (a^(2) - 5a + 6)x^(3) + (a^(2) -3a+ 2)x + (a^(3) -1) AA x in R The number of values of a for which f(x) = g(x) AA x in R

f:R rarr R defined by f(x)=(x)/(x^(2)+1),AA x in R is

If the sum of the cubes of zeroes of the polynomial x^(3)-5x^(2)+k^(2)x+8 is 71 ,then sqrt(k)=

Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral value of k for which f (x) le k AA x in R is

The set of values of k for which kx^(2)-x-k+1<0AA x in R, is

Find the value(s) of k, if one of the zeroes of the polynomial f(x) = (k^2 +8)x^2 + 13x + 6k is reciprocal of the other.