Saved Bookmarks
| 1. |
Solve the equation \( x^{3}-3 x^{2}+4=0 \), given that two of its roots are equal. |
|
Answer» Given equation is x3 - 3x2 + 4 = 0 \(\because\) x = -1 satisfies the equation. (Because, (-1)3 - 3(-1)2 + 4 = -1 - 3 + 4 = -4 + 4 = 0) \(\therefore \) (x + 1) is a factor of x3 - 3x2 + 4. Now, since x3 - 3x2 + 4 = 0 ⇒ (x + 1) (x2 - 4x + 4) = 0 ⇒ (x + 1) (x - 2)2 = 0 ⇒ x = -1, 2, 2 Hence, roots of given equation are -1, 2, 2. |
|