We solve the relationship distance = speed × time using a quadratic equation.
📘 Example ①
Traveling a certain distance at a speed of x km per hour takes x hours. The distance is (x² − 5x) km, and the actual distance is 6 km. Find x.
Answer:x² − 5x = 6 → x² − 5x − 6 = 0 → (x−6)(x+1) = 0 → x = 6（positive number）
Traveling a certain distance at a speed of x km per hour takes x hours. The distance is (x² − 5x) km, and the actual distance is 6 km. Find x.
Answer:x² − 5x = 6 → x² − 5x − 6 = 0 → (x−6)(x+1) = 0 → x = 6（positive number）
💡 Key Point
- Speed, time, and distance are positive → discard the negative solution
- Express “distance = speed × time” as an equation
Practice Problems
- A rectangle has a length of x m and a width of (x + 3) m. If its area is 28m², find x.
Answers and Explanations
- Answer:x = 4。x(x+3)=28 → x²+3x−28=0 → (x+7)(x−4)=0 → x=4。