Saved Bookmarks
| 1. |
If `a, b, c` are in `GP`, then the equations `ax^2 +2bx+c = 0` and `dx^2 +2ex+f =0` have a common root if `d/a , e/b , f/c `are inA. APB. GPC. HPD. None of these |
|
Answer» Correct Answer - A Given that a,b,c are GP. Then, `b^(2)=ac " " "…..(i)"` and equations `ax^(2)+2ex+c=0` and `dx^(2)+2ex+f=0 " have a common root. ""………..(A)"` Now, `ax^(2)+2bx+c=0` `implies ax^(2)+2sqrt(ac)" " x+c=0 " " [" by Eq. (i) "]` `implies (sqrt(ax)+sqrt(c ))^(2)=0 " " implies sqrt(ax)+sqrt(c )=0` `implies x=-(sqrt(c ))/(sqrt(a)) " " [" repeated "]` By the condition `(A), (-(sqrt(c ))/(sqrt(a)))` be the root of `dx^(2)-2ex+f=0` So, it saftisfy the equation `d(-sqrt(c/(a)))^(2)+2e(-sqrt(c/(a)))+f=0` ` implies (dc)/(a)-2esqrt(c/(a))+f=0 " " implies (d)/(a)-(2e)/(sqrt(ac))+(f)/(c )=0` ` implies (d)/(a)-(2e)/(b)+(f)/(c )=0 " " implies (d)/(a)+(f)/(c )=2((e)/(b))` So, `(d)/(a),(e)/(b),(f)/(c )` are in AP. |
|