If p is a constant and `f(x) =|(x^2,x^3,x^4),(2,3,6),(p,p^2,p^3)|` if `f'(x)=0` have roots `alpha,beta` , then

If P(x) is a polynomial degree four with leading coefficient one such that P(1)=2,P(2)=6,P(3)=12,P(4)=20. Also P(x)=0 has roots alpha, beta, gamma and delta . Then the value of ((alpha+3)(beta+3)(gamma+3)(delta+3))/(100)

Consider the function f(x)=|{:(x^(3),sinx,cosx),(6,-1,0),(p,p^2,p^(3)):}| where p is a constant. What is the value of p for which f''(0)=0 ?

Cosider the function f(x)=|{:(x^(3),sin x,cos x),(6,-1,0),(p,p^(2),p^(3)):}| , where p is a constant. What is the value of p for which f''(0) = 0 ?

Cosider the function f(x)=|{:(x^(3),sin x,cos x),(6,-1,0),(p,p^(2),p^(3)):}| , where p is a constant. What is the value of f'(0) ?

If f(x)=|{:(x^(3),x^(4),3x^(2)),(1,-6,4),(p,p^(2),p^(3)):}| , where p is a constant, then (d^(3))/(dx^(3))(f(x)) , is

If f(x)=|{:(x^(3),x^(4),3x^(2)),(1,-6,4),(p,p^(2),p^(3)):}| , where p is a constant, then (d^(3))/(dx^(3))(f(x)) , is

Consider the quadratic polynomial 'f(x)=x^(2)-px+q' where 'f(x)=0' has prime roots alpha and beta and 'p=alpha+beta' , 'q=alpha beta' .If 'p+q=11' and 'a=p^(2)+q^(2)' then find the value of 'f(a)/100' where a is an odd positive integer.