If the normal to the parabola `y^(2)=4ax` at points `(ap^(2),2ap),(aq^(2),2aq),and(ar^(2),2ar)` are concurrent then the common root of equations `px^(2)+qx+r=0and a(b-c)x^(2)+b(c-a)x+c(a-b)=0` is

If the normals to the parabola y^2=4a x at three points (a p^2,2a p) and (a q^2,2a q) and (a r^2,2ar) are concurrent, then the common root of equations P x^2+q x+r=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 is (a) p (b) q (c) r (d) 1

If the normals to the parabola y^2=4a x at three points (a p^2,2a p), and (a q^2,2a q) are concurrent, then the common root of equations P x^2+q x+r=0 and a(b-c)x^2+b(c-a)x+c(a-b)=0 is p (b) q (c) r (d) 1

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If sectheta+ tantheta = 1 , then root of the equation (a-2b + c)x^2 +(b-2c+ a)x+(c-2a+b) = 0 is:

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a) x-a=0 are :

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in A.P 2p^3 - 9 pq + 27 r=0

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.