upteto17 q125
0. If the roots, of the equation x2 - px + 54= 0 are in the ratio 2 : 3, then the value of p is
- Option : D
- Explanation : (D) Given, equation x2 - px + 54 = 0
Let roots of the given equation are 2α and 3α
Then, 2α + 3α = p ⇒ 5α = p ⇒ α = p / 5
and also, (2α)(3α) = 54
⇒ 6(α)2 = 54
⇒ 6(p/5)2 = 54 (∴ α = p/5)
⇒ 6 × p2/25 = 54 ⇒ p2 = 9 × 25
⇒ p = 3 × 5 = 15
