Saved Bookmarks
| 1. |
Let p and q be the roots of the quadratic equation ` x^(2) - (alpha - 2) x -alpha - 1 = 0`. What is the minimum possible value of ` p^(2) + q^(2)` ? |
|
Answer» Correct Answer - D Given equation is ` x^(2) - (alpha - 2) x - alpha - 1= 0` Sum of the roots, `p+q= alpha -2` Product of the roots pq ` =- alpha -1` Now, `p^(2) + q^(2) = (p+q)^(2) - 2pq` ` = (alpha-2)^(2) + 2 (alpha+ 1)` ` = alpha^(2) + 4 - 4alpha+2alpha+2 = (alpha-1)^(2) + 5` Hence, the minimum balue of `p^(2) + q^(2) ` will be 5 |
|