" 21."(x^(2))/((p+qx)^(2))

If P=21(21^(2)-1^(2))(21^(2)-2^(2))...(21^(2)-10^(2)) , then p is divisible by-

Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} then:

Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} then:

int(px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1)dx

Solve for x and y, px + qy = 1 and qx + py = ((p + q)^(2))/(p^2 + q^2)-1 .

If alpha and beta are the zeros of the polynomial f(x)=x^(2)+px+q, then a polynomial having (1)/(alpha) and (1)/(beta) is its zeros is (a) x^(2)+qx+p( b) x^(2)-px+q(c)qx^(2)+px+1 (d) px^(2)+qx+1

If (x+2) is a common factor of (px^(2)+qx+r) and (qx^(2)+px+r) then a p=q or p+q+r=0 b p=r or p+q+r=0 c) q=r or p+q+r=0 d p=q=-(1)/(2)r

The expression x^(2)-4px+q^(2)>0 for all real x and also r^(2)+p^(2)

If (x)/((x-1)(x^(2)+1)^(2))=(P)/(x-1)+(Qx+R)/(x^(2)+1)+(Sx+T)/((x^(2)+1)^(2)) , then P+Q-R-S+T= ____________.