f(x)=prod_(k=1)^(999)(x^(2)-47x+k)," then product of all real roots of "f(x)=0" is "

If f(x)=Pi_(k=1)^(999)(x^(2)-47x+k) . then product of all real roots of f(x)=0 is

If f(x)=Pi_(k=1)^(999)(x^(2)-47x+k) . then product of all real roots of f(x)=0 is

If f(x) = sum_(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)) , then the product of root of f(x) = 0 as n rarr oo , is

f(x)=prod_(r=1)^(5)(x+r), then f'(-5) is

Let f(x) be a polynomial with real coefficients such that f(0)=1 and for all x ,f(x)f(2x^(2))=f(2x^(3)+x) The number of real roots of f(x) is:

If f(x)=x^(3)-3x+1, then the number of distinct real roots of the equation f(f(x))=0 is

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are