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Answer:
1. For the equation 5x² - 15x = 0:
First, factor out x: x(5x - 15) = 0
This equation can be rewritten as x(5(x - 3)) = 0
So, x = 0 or x - 3 = 0
Therefore, x = 0 or x = 3
Checking:
For x = 0: 5(0)² - 15(0) = 0, which is true.
For x = 3: 5(3)² - 15(3) = 45 - 45 = 0, which is also true.
2. For the equation 4x² = 16:
Divide both sides by 4: x² = 4
Taking the square root of both sides: x = ±√4
So, x = ±2
Checking:
For x = 2: 4(2)² = 16, which is true.
For x = -2: 4(-2)² = 16, which is also true.
3. For the equation 2x² - 12 = 0:
Add 12 to both sides: 2x² = 12
Divide by 2: x² = 6
Taking the square root of both sides: x = ±√6
Checking:
For x = √6: 2(√6)² - 12 = 2(6) - 12 = 0, which is true.
For x = -√6: 2(-√6)² - 12 = 12 - 12 = 0, which is also true.
So, the solutions to the quadratic equations are: