Math Problem Statement

Tentukan penyelesaian setiap persamaan kuadrat di bawah ini dengan memfaktorkan!

Solution

The image contains several quadratic equations and algebraic problems. Let me walk through some of them:

1. Tentukan penyelesaian setiap persamaan kuadrat di bawah ini dengan memfaktorkan!

a. 2x24x=02x^2 - 4x = 0

We can factor out the common term: 2x(x2)=02x(x - 2) = 0 The solutions are: x=0orx=2x = 0 \quad \text{or} \quad x = 2

b. 3x28x+10=03x^2 - 8x + 10 = 0

This equation doesn’t factor easily, so we might need to use the quadratic formula.

2. Tentukan mm dari penyelesaian persamaan x27x+m=0x^2 - 7x + m = 0 jika salah satu akar persamaannya adalah 4.

We use the fact that if 4 is a root, we can substitute it into the equation: 427(4)+m=01628+m=0m=124^2 - 7(4) + m = 0 \quad \Rightarrow \quad 16 - 28 + m = 0 \quad \Rightarrow \quad m = 12

Would you like more detailed solutions for all the problems, or further steps for specific questions?

Here are some related questions for further practice:

  1. How do you factor quadratic equations with no common factor?
  2. Can all quadratic equations be solved by factoring? If not, what other methods exist?
  3. What is the quadratic formula, and when is it useful?
  4. How can the discriminant help in determining the number of solutions for a quadratic equation?
  5. How do you solve quadratic equations by completing the square?

Tip: Always check if you can factor out a common term before using other methods like the quadratic formula.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Factoring

Formulas

Quadratic equation formula ax^2 + bx + c = 0
Factoring (a-b)(a+b)

Theorems

Factoring Theorem
Quadratic Formula

Suitable Grade Level

Grades 9-10