If `x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b)` have a common root, then prove that their other roots satisfy the equation `x^2+c x+a b=0.`

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 . Also, show that their other roots are the roots of the equation x^2+x+p q=0.

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a common root, then a:b:c is

a ,b ,c are positive real numbers forming a G.P. ILf a x 62+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

If 2a+3b+6c=0, then prove that at least one root of the equation a x^2+b x+c=0 lies in the interval (0,1).

For a ne b , if the equation x^(2)+ax+b=0" and "x^(2)+bx+a=0 have a common root, then the value of a+b=

If 8 and 2 are the roots of x^(2) + ax + c = 0 and 3,3 are the roots of x^(2) + dx + b = 0, then the roots of the equation x^(2) + ax + b = 0 are