Single correct option
If the roots of the equation x² − px + q = 0 are two consecutive integers, then p² − 4q equals:
- A. 0
- B. 1
- C. 2
- D. 4
Show answer and solution
Answer: (B) 1
Let the roots be a and a + 1. Then p = sum = 2a + 1 and q = product = a(a + 1).
p² − 4q = (2a + 1)² − 4a² − 4a = 1.
Conceptually, p² − 4q is the discriminant, and it equals (difference of roots)². Consecutive integers differ by 1, so the answer is 1² = 1.
Tip: (α − β)² = (α + β)² − 4αβ.
p² − 4q = (2a + 1)² − 4a² − 4a = 1.
Conceptually, p² − 4q is the discriminant, and it equals (difference of roots)². Consecutive integers differ by 1, so the answer is 1² = 1.
Tip: (α − β)² = (α + β)² − 4αβ.
Saved on this device. Sign in or create a free account to keep it on every device.