if `alpha and beta` are the roots of equation `x^2+5sqrt2x+10=0 , P_n=alpha^n - beta^n , (P_17P_20+5sqrt2)/(P_18P_19+5sqrt2)(P_17P_19)/P_18^2=?`

If alpha,beta are the roots of the equation x^(2)-p(x+1)-c=0, then (alpha+1)(beta+1)=

If alpha and beta are the roots of the equation x^(2)-px +16=0 , such that alpha^(2)+beta^(2)=9 , then the value of p is

If alpha and beta are the roots of the equation x^(2)+px+(3p)/(4)=0 such that | alpha-beta|=sqrt(10) then p belongs to the set

If alpha and beta are the roots of x^(2)-3px+p^(2)=0 such that alpha^(2)+beta^(2)=(7)/(4) then values of p are

If alpha,beta are roots of the equation x^(2)+5(sqrt(2))x+10=0,alphagtbetaandP_(n)=alpha^(n)-beta^(n) for each positive integer n , then the value of ((P_(17)P_(20)+5sqrt(2)P_(17)P_(19))/(P_(18)P_(19)+5sqrt(2)P_(18)^(2))) is equal to ________.

Let alpha and beta be the roots of a quadratic equation 4x^(2)-(5p+1)x+5p=0. If beta=1+alpha, then the integral value of p, is