Single correct option
The roots of the equation x² − 15x + k = 0 are in the ratio 2 : 3. What is the value of k?
- A. 45
- B. 54
- C. 60
- D. 36
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Answer: (B) 54
Let the roots be 2a and 3a. Their sum = 5a = 15, so a = 3 and the roots are 6 and 9.
The product of roots = k = 6 × 9 = 54.
Tip: For x² − Sx + P = 0 with roots in ratio m : n, P = mn·S²/(m + n)² = 6 × 225/25 = 54.
The product of roots = k = 6 × 9 = 54.
Tip: For x² − Sx + P = 0 with roots in ratio m : n, P = mn·S²/(m + n)² = 6 × 225/25 = 54.
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