Show that one of the roots of equation `ax^2+bx+c=0` may be reciprocal of one of the roots of `a_1x^2+b_1x+c_1=0 if (aa_1-c``c_1)^2=(bc_1-ab_1)(b_1c-a_1b)`

If one of the roots of the equation ax^2 + bx + c = 0 be reciprocal of one of the a_1 x^2 + b_1 x + c_1 = 0 , then prove that (a a_1-c c_1)^2 =(bc_1-ab_1) (b_1c-a_1 b) .

The roots of a_1x^2+b_1x + c_1=0 are reciprocal of the roots of the equation a_2x^2 +b_2x+c_2=0 if

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

Suppose 1,2,3 are the roots of the equation x^4 + ax^2 + bx + c = 0 . Find the value of c.

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

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1//cdot

If one root of the equation 2x^2+k x-6=0 is 2, then the other root is (a) 6 (b) -6 (c) -1 (d) 1

Let alpha,beta be the roots of the quadratic equation ax^2+bx+c=0 then the roots of the equation a(x+1)^2+b(x+1)(x-2)+c(x-2)^2=0 are:-

If a,b,c in R and the equation ax^2+bx+c = 0 and x^2+ x+ 1=0 have a common root, then