Let a,b,c,p,q be the real numbers. Suppose `alpha,beta` are the roots of the equation `x^2 +px +q =0` and `alpha, beta/2` are the roots of the equation `ax^2 +bx +c =0` where `beta^2 !in {-1,0,1}.`

Let a, b, c, p, q be the real numbers. Suppose alpha,beta are the roots of the equation x^2+2px+ q=0 . and alpha,1/beta are the roots of the equation ax^2+2 bx+ c=0 , where beta !in {-1,0,1} . Statement I (p^2-q) (b^2-ac)>=0 Statement 2 b != pa or c != qa .

Let a, b, c, p, q be the real numbers. Suppose alpha,beta are the roots of the equation x^2+2px+ q=0 . and alpha,1/beta are the roots of the equation ax^2+2 bx+ c=0 , where beta !in {-1,0,1} . Statement I (p^2-q) (b^2-ac)>=0 Statement 11 b !in pa or c !in qa .

If alpha,beta are the roots of the equation x^(2)+px+q=0, then -(1)/(alpha),-(1)/(beta) are the roots of the equation.

If alpha. beta are roots of the equation ax^(2)+bx+c=0 and alpha-beta=alpha*beta then

IF alpha and beta be the roots of the equation x^2+px+q=0 show that alpha/beta is a root of the equation qx^2-(p^2-2q)x+q=0 .

If alpha and beta ( alpha

alpha and beta are the roots of the equation ax^(2)+bx+c=0 and alpha^(4) and beta^(4) are the roots of the equation lx^(2)+mx+n=0 if alpha^(3)+beta^(3)=0 then 3a,b,c

Let alpha, beta in R. If alpha, beta^(2) are the roots of quadratic equation x^(2) - px + 1 = 0 and alpha^(2), beta are the roots of quadratic equation x^(2) -px + 8 = 0 , then find p, q , alpha, beta .

If alpha,beta are the roots of the equation x^(2)+px+q=0, then -(1)/(alpha),-(1)/(beta) are the roots of the equation x^(2)-px+q=0 (b) x^(2)+px+q=0( c) qx^(2)+px+1=0 (d) q^(2)-px+1=0