If the roots of the equation `(1-q+p^2/2)x^2+p(1+q)x+q(q-1)+p^2/2 =0` are equal then show that `p^2=4q.`

If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in A.P.

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show that 1/p+1/r=2/q .

If p ,q are real p!=q , then show that the roots of the equation (p-q)x^2+5(p+q)x-2(p-q)=0 are real and unequal.

If p,q are real p!=q, then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q)=0 are real and unequal.

If p, a,rare real and p!=q ,then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q)=0 are real and unequal.