2026 · Q6
If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q)?
Elementary MathematicsHCF and LCM
- A-23
- B-17
- C17
- D23
Explanation
Since (x−5) is a factor of both polynomials, substituting x=5 must annihilate each. From x²−x−p: 25−5−p=0 gives p=20; from x²−qx−10: 25−5q−10=0 gives q=3. Therefore p+q=23, option D.