If minimum value of `x^(2)-2px+p^(2)-1` is equal to `3AA x>=0` then p cannot be

Let f(x)=x^(2)+2px+2q^(2) and g(x)=-x^(2)-2px+p^(2) (where q ne0 ). If x in R and the minimum value of f(x) is equal to the maximum value of g(x) , then the value of (p^(2))/(q^(2)) is equal to

The minimum value of (x-p)^(2) + (x-q)^(2) + (x-r)^(2) will be at x equals to

Let P(x) and Q(x) be two quadratic polynomials such that minimum value of P(x) is equal to twice of maximum value of Q(x) and Q(x)>0AA x in(1,3) and Q(x)<0AA x in(-oo ,1)uu(3, oo) If sum of the roots of the equation P(x) =0 is 8 and P(3)-P(4)=1 and distance between the vertex of y=P(x) and vertex of y=Q(x) is 2sqrt(2) The polynomial P(x) is:

Let P(x) and Q(x) be two quadratic polynomials such that minimum value of P(x) is equal to twice of maximum value of Q(x) and Q(x)>0AA x in(1, 3) and Q (x)<0AA x in(-oo, 1)uu(3, oo) . If sum of the roots of the equation P(x)=0 is 8 and P(3)-P(4)=1 and distance between the vertex of y=P(x) and vertex of y=Q(x) is 2sqrt(2) The polynomial P(x) is:

The minimum value of a^(cos^(2)x)+a^(sin^(2)x)AA(a>0) is

Let P(x)=x^(2)+2(a^(2)+a+1)x+a^(2)+5a+2 If minimum value of P(x) for x<=0 is 8, thernthe sum ofthe squares of all possible value(s)of a,is

If the quadratic equation x^(2)-px+q=0 where p, q are the prime numbers has integer solutions, then minimum value of p^(2)-q^(2) is equal to _________

find values of p if f(x)=cos x-2px is invertible.

12x^(2)+px+2=0 Find the value of P