Selesaikanlah persamaan kuadrat di bawah ini dengan pemfaktoran. a. x^2 - 3x - 28 = 0 b. x^2 - 5x...

Summary

This video provides a step-by-step guide to solving quadratic equations through factoring. The script demonstrates how to solve various quadratic equations by identifying two numbers that multiply to give the constant term and add to the middle coefficient. Each example is broken down, showing how to factorize the equation and find the values of x. The video covers different cases, including those where the coefficient of x² is not 1, and emphasizes techniques such as simplifying terms and using common factors. The final solutions for each equation are clearly presented for easy understanding.

Takeaways

• 😀 The script explains how to solve quadratic equations using factoring methods.
• 😀 For each example, the goal is to find the values of x that make the quadratic equation true.
• 😀 The script uses the standard form of a quadratic equation: ax² + bx + c = 0.
• 😀 To factor a quadratic equation, find two numbers (p and q) that multiply to c and add to b.
• 😀 Example A: x² - 3x - 28 = 0 is factored into (x - 7)(x + 4) = 0, giving solutions x = 7 and x = -4.
• 😀 Example B: x² - 5x - 14 = 0 is factored into (x - 7)(x + 2) = 0, giving solutions x = 7 and x = -2.
• 😀 Example C: x² - 9x + 20 = 0 is factored into (x - 5)(x - 4) = 0, giving solutions x = 5 and x = 4.
• 😀 Example D: x² - 10x + 24 = 0 is factored into (x - 6)(x - 4) = 0, giving solutions x = 6 and x = 4.
• 😀 Example E: x² - 18x + 32 = 0 is factored into (x - 16)(x - 2) = 0, giving solutions x = 16 and x = 2.
• 😀 For non-standard forms, the script demonstrates how to transform the equation into a solvable form, like dividing both sides by 4 in Example G.
• 😀 The script concludes with an example involving fractions, showing how to factor and solve equations with non-integer coefficients.

Q & A

What is the goal when solving quadratic equations using factoring?

The goal is to find the value of x that satisfies the quadratic equation, making it true, i.e., solving for x such that the equation equals zero.

How can we factor a quadratic equation of the form ax² + bx + c = 0?

To factor a quadratic equation, we look for two numbers, p and q, that multiply to give c (the constant term) and add up to give b (the coefficient of x). This allows us to express the equation as (x + p)(x + q) = 0.

In the example x² - 3x - 28 = 0, how are the values of p and q determined?

The two numbers that multiply to -28 and add up to -3 are -7 and 4. Therefore, the equation factors as (x - 7)(x + 4) = 0.

What is the solution to the equation x² - 3x - 28 = 0?

The solutions are x = 7 or x = -4, since either factor (x - 7) or (x + 4) must equal zero.

For the equation x² - 5x - 14 = 0, how do we find the factors?

We need to find two numbers that multiply to -14 and add up to -5. The correct pair is -7 and 2, so the equation factors as (x - 7)(x + 2) = 0.

What are the solutions to the equation x² - 5x - 14 = 0?

The solutions are x = 7 or x = -2.

What should we do if the coefficient a is not equal to 1 in a quadratic equation?

If a is not equal to 1, we can either factor out the greatest common divisor (if possible) or divide the entire equation by a to simplify it into a form where a equals 1.

How do we factor the equation 4x² + 13x - 12 = 0?

First, we divide the whole equation by 4 to make the coefficient of x² equal to 1. This results in x² + (13/4)x - 3 = 0, and we then find the pair of numbers that multiply to -3 and add to 13/4. These numbers are 4 and -3/4, so the factored form is (x + 4)(x - 3/4) = 0.

What are the solutions to the equation 4x² + 13x - 12 = 0 after factoring?

The solutions are x = -4 or x = 3/4, based on the factored form of the equation.

In the equation 45x² + 0x - 80 = 0, how do we proceed to factor it?

We first rewrite the equation as 45x² + 0x - 80 = 0, then divide both sides by 45 to simplify the equation to x² + 0x - 16/9 = 0. After finding the pair of numbers that multiply to -16/9 and add to 0, the factors are (x - 4/3)(x + 4/3) = 0.

What are the solutions to the equation 45x² + 0x - 80 = 0 after factoring?

The solutions are x = 4/3 or x = -4/3.