If `alpha` and `beta` (`alpha'<'beta') are the roots of the equation `x^2+b x+c=0,` where `c<0

If alpha ne beta but alpha^(2)= 5 alpha - 3 and beta ^(2)= 5 beta -3 then the equation having alpha // beta and beta // alpha as its roots is :

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If alpha != beta but, alpha^(2) = 4alpha - 2 and beta^(2) = 4beta - 2 then the quadratic equation with roots (alpha)/(beta) and (beta)/(alpha) is

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta)+(beta)/(alpha)) then N=

If alpha and beta are the roots of 2x^(2) + 5x - 4 = 0 then find the value of (alpha)/(beta) + (beta)/(alpha) .

Given alpha and beta are the roots of the quadratic equation x^(2)-4x+k=0(kne0). If alpha beta, alpha beta^(2)+alpha^(2)beta and alpha^(3)+beta^(3) are in geometric progression, then the value of k is equal to

If alpha and beta are the zeros of the quadratic polynomial f(x)=a x^2+b x+c , then evaluate: (i) beta/(aalpha+b)+alpha/(abeta+b) (ii) a((alpha^2)/beta+(beta^2)/alpha)+b(alpha/beta+beta/alpha)

If cos(alpha+beta)+sin(alpha-beta)=0 and tan beta ne1 , then find the value of tan alpha .

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of (1)/(alpha beta)+(alpha+beta) is