Saved Bookmarks
| 1. |
If the equation \( x^{2}+a x+b=0 \) has roots \( 12 \sin a \) and \( 5 \cos a \forall a \in R \) then |
|
Answer» Sum of roots = 12sin a + 5cos a = -a Product of roots = (12sin a)(5sin a) = b ⇒ 12sin a +5cos a = -a .....(i) and 60sin a cos a = b .....(ii) Squaring equation (1), we get 144sin2a + 25cos2a + 120sin a cos a = a2 ⇒ 144sin2a + 25(1 -sin2a) + 2b = a2 (From(i)) ⇒ 119 sin2a = a2 - 2b - 25 ⇒ sin2a = \(\frac{a^2 - 2b - 25}{119}\) but 0 \(\le\) sin2a \(\le\) 1 ⇒ 0 \(\le\) a2 - 2b - 25 \(\le\) 119 ⇒ 0 \(\le\) a2 - 2b \(\le\) 144 |
|