If the ratio of the roots of `a x ^2+2b x+c=0` is same as the ratios of roots of `p x^2+2q x+r=0,` then a.`(2b)/(a c)=(q^2)/(p r)` b. `b/(a c)=(q^)/(p r)` c. `(b^2)/(a c)=(q^2)/(p r)` d. none of these

If the ratio of the roots of x^(2) + bx + c = 0 is equal to the ratio of the roots of x^(2)+px+q=0 , then p^(2)c-b^(2)q=

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^(2)c=b^2qdot

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0t h e nh= -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/q-q/p) d. none of these

If (x_1, y_1)&(x_2,y_2) are the ends of a diameter of a circle such that x_1&x_2 are the roots of the equation a x^2+b x+c=0 and y_1&y_2 are the roots of the equation p y^2=q y+c=0. Then the coordinates of the centre of the circle is: (b/(2a), q/(2p)) ( b/(2a), q/(2p)) (b/a , q/p) d. none of these

If a+b+c=0 , prove that the roots of ax^(2)+bx+c=0 are rational. Hence, show that the roots of (p+q)x^(2)-2px+(p-q)=0 are rational.

If alpha,beta are the roots of x^2+p x+q=0 and gamma,delta are the roots of x^2+p x+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= (a) \ 1 (b) \ q (c) \ r (d) \ q+r

For p, q in R , the roots of (p^(2) + 2)x^(2) + 2x(p +q) - 2 = 0 are

If alpha,beta are real and distinct roots of a x^2+b x-c=0a n dp ,q are real and distinct roots of a x^2+b x-|c|=0,w h e r e(a >0), then (a) alpha,beta in (p ,q) (b). alpha,beta in [p ,q] (c). p ,q in (alpha,beta) (d). none of these

If the difference of the roots of x^2-p x+q=0 is unity, then a) p^2+4q=1 b) p^2-4q=1 c) p^2+4q^2=(1+2q)^2 d) 4p^2+q^2=(1+2p)^2