If one root of the quadratic equation `ax^(2) + bx + c = 0 ` is equal to the `n^(th)` power of the other root , then show that `(ac^(n))^(1/(n+1)) + (a^(n)c)^(1/(n+1))+b = 0 `

If one root of the equation ax^2 + bx + c = 0 is equal to the n^(th) power of the other, then (ac^n)^(1/(n+1)) + (a^nc)^(1/(n+1)) + b is equal to

If the ratio of the roots of the equation ax^(2)+bx+c=0 is m: n then

If the roots of the equation ax^(2)+bx+c=0 are in the ratio m:n then

If one root is the n^("th") power of the other root of the equation x^(2) -ax + b = 0 then b^((n)/(n+1))+b^((1)/(n+1)) =

Find the condition that one root of the quadratic equation ax^(2)+bx+c=0 shall be n times the other, where n is positive integer.

If the ratio of the roots of the equation ax^2+bx+c=0 is equal to ratio of roots of the equation x^2+x+1=0 then a,b,c are in

if alpha&beta are the roots of the quadratic equation ax^2 + bx + c = 0 , then the quadratic equation ax^2-bx(x-1)+c(x-1)^2 =0 has roots

In quadratic equation ax^(2)+bx+c=0 , if discriminant D=b^(2)-4ac , then roots of quadratic equation are:

If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbeta ils a real root of - a x^2+b x+c=0, then show that there is a root gamma of equation (a//2)x^2+b x+c=0 whilch lies between aa n dbetadot

If alphaa n dbeta are roots of the quadratic equation a x^2+b x+c=0 and a+b+c >0,a-b+c >0&c<0,t h e n[alpha]+[beta] is equal to (where [dot] denotes the greatest integer function) (a) 10 (b) -3 (c) -1 (d) 0