Fix the mistake: Applications of Quadratic Equations
Applications of Quadratic Equations ① Procedure for Word Problems
Procedure for solving word problems using a quadratic equation: ① Choose x ② Set up an equation ③ Solve it ④ Check the conditions.
📘 Example ①
The square of a number x is 4 greater than three times the number. Find x.
Answer:x² = 3x + 4 → x² − 3x − 4 = 0 → (x−4)(x+1) = 0 → x = 4 or −1
The square of a number x is 4 greater than three times the number. Find x.
Answer:x² = 3x + 4 → x² − 3x − 4 = 0 → (x−4)(x+1) = 0 → x = 4 or −1
💡 Key Points
- Let x represent terms such as “a number” or “an integer”
- Use only the solutions that satisfy the conditions of the problem (positive numbers, natural numbers, and so on)
Practice Problem
- There are two consecutive positive integers whose product is 56. Find the two integers.
Answer and Explanation
- Answer:7 and 8. Let the smaller number be x: x(x+1)=56 → x²+x−56=0 → (x+8)(x−7)=0 → x=7 (a positive integer).
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