InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If roots of equation `x^3-2c x+a b=0`are real and unequal, then prove that the roots of `x^2-2(a+b)x+a^2+b^2+2c^2=0`will be imaginary. |
|
Answer» Roots pf eqution `x^(2) - 2cx + ab = 0` are real and unequal `therefore D_(1) gt 0` `therefore 4c^(2) - 4ab gt 0` or `c^(2) - ab gt 0` (1) For equation `x^(2) - 2 (a + b) x + (a^(2) + b^(2) + 2c^(2))=0` `D_(2) = 4 (a + b)^(2) - 4 (a^(2) + b^(2) + 2c^(2))` = `- 8 ((c^(2) - ab) lt 0 (from (1))` Therefoue , roots are imaginary. |
|