Math Problem Statement

Tentukan nilai a, b, dan c dari persamaan kuadrat berikut: a. x^2 + 2x - 2 = 0 b. -x^2 - x - 1 = 0 c. -3x^2 + 3 - 3x = 0

Solution

The image contains three quadratic equations where you are asked to find the values of aa, bb, and cc for each equation. These values correspond to the coefficients in the standard quadratic form ax2+bx+c=0ax^2 + bx + c = 0.

Let's analyze each equation:

a. x2+2x2=0x^2 + 2x - 2 = 0

  • Comparing this with the standard form ax2+bx+c=0ax^2 + bx + c = 0:
    • a=1a = 1 (coefficient of x2x^2),
    • b=2b = 2 (coefficient of xx),
    • c=2c = -2 (constant term).

b. x2x1=0-x^2 - x - 1 = 0

  • Comparing this with ax2+bx+c=0ax^2 + bx + c = 0:
    • a=1a = -1,
    • b=1b = -1,
    • c=1c = -1.

c. 3x2+33x=0-3x^2 + 3 - 3x = 0

  • Rewriting this as 3x23x+3=0-3x^2 - 3x + 3 = 0, we have:
    • a=3a = -3,
    • b=3b = -3,
    • c=3c = 3.

If you need further details or have any questions, feel free to ask!

Here are five related questions to expand on this:

  1. How do you solve a quadratic equation using the quadratic formula?
  2. Can you factor these quadratic equations to find their roots?
  3. How does the discriminant help in determining the number of solutions for a quadratic equation?
  4. What are the steps to complete the square for solving a quadratic equation?
  5. What is the graphical representation of these quadratic equations?

Tip: Always check the signs of the coefficients carefully when comparing an equation to the standard form ax2+bx+c=0ax^2 + bx + c = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations

Formulas

Standard form of quadratic equation: ax^2 + bx + c = 0

Theorems

Quadratic equation structure

Suitable Grade Level

Grades 7-9