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

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 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 n h= a. -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/a-q/p) d. none of these

IF p^2/q and q^2/p are the roots of the equation 2x^2+7x-4=0 , find the equation whose roots are p and q (p+q real).

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

If p and q are the roots of the equation 3x^2+6x+2=0 , show that the equation whose roots are (-p^2/q) and (-q^2/p) is 3x^2-18x+2=0 .

If alpha,beta are real and distinct roots of a x^2+b x-c=0 and p ,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

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

In the equation x^2-px+q=0 ratio of the roots are 2:3 ,then prove that 6p^2=25q

The base B C of a A B C is bisected at the point (p ,q) & the equation to the side A B&A C are p x+q y=1 & q x+p y=1 . The equation of the median through A is: (p-2q)x+(q-2p)y+1=0 (p+q)(x+y)-2=0 (2p q-1)(p x+q y-1)=(p^2+q^2-1)(q x+p y-1) none of these

If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^(2) – 12x + q = 0 , where a,b,c,d form a G.P Prove that (q+q):(q-p) = 17 : 15