The product of the sines of the angles of a triangle is `p` and the product of their cosines is `qdot` Show that the tangents of the angles are the roots of the equation `q x^3-p x^2+(1+q)x-p=0.`

If p and q are the roots of the equation x^(2)+px+q=0 , then

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

If the sides of a right angled triangle are in A.P then the sines of the acute angles are

The solution set of the equation pqx^(2)-(p+q)^(2)x+(p+q)^(2)=0 is

Show that , if p,q,r are rational , the roots of the equation x^2-2px+p^2-q^2+2pr-r^2=0 are rational .

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 . Also, show that their other roots are the roots of the equation x^2+x+p q=0.

IF the sides of the triangle are p , q sqrt(p^2 + q^2 + pq) then the largest angle is

If one root is square of the other root of the equation x^2+p x+q=0 then the relation between p and q is

If the roots of the equation q^(2)x^(2)+p^(2)x+r^(2)=0 are the squares of the roots of the equation qx^(2)+px+r=0 , are the squares of the roots of the equation qx^(2)+px+r=0 , then q, p, r are in: