`P(y)=y^2-y+1`the value of `P(0)`is

If alpha and beta are the zeros of the quadratic polynomial p(y)=5y^2-7y+1 , find the value of 1/alpha+1/beta .

if p = (4xy)/(x + y) , find the value of (p+2x)/(p-2x) + (p+2y)/(p-2y) .

If 2p=x+1/x and 2q=y+1/y , then the value of ((pq+sqrt((p^2-1)(q^2-1)))/(xy+1/(xy))) is

The line y=mx+1 touches the curves y=-x^(4)+2x^(2)+x at two points P(x_(1),y_(1)) and Q(x_(2),y_(2)) . The value of x_(1)^(2)+x_(2)^(2)+y_(1)^(2)+y_(2)^(2) is

If y=2^(2p-1) and z=p-2, what is the value of (y)/(z) when p=2.5 ?

If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,\ -1) , find the values of a and b and show that y is maximum at P .

A parabola (P) touches the conic x^2+xy+y^2-2x-2y+1=0 at the points when it is cut by the line x+y+1=0. If (a,b) is the vertex of the parabola (P), then the value of |a-b| is

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the value of (1)/(y_(1))+(1)/(y_(2)) is

If x=(sin^3P)/cos^2P,y=cos^3P/sin^2P" and " sinP+cosP=1/2 then find the value of x + y.

If the normal to the ellipse x^2/25+y^2/1=1 is at a distance p from the origin then the maximum value of p is