The roots of the equation 5x^2 - 20x + 15 = 0 are:

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Question: The roots of the equation 5x^2 - 20x + 15 = 0 are:

Options:

Correct Answer: 2

Solution:

Using the quadratic formula, the roots are x = [20 ± √(400 - 300)] / 10 = [20 ± 10] / 10 = 3 and 1.

The roots of the equation 5x^2 - 20x + 15 = 0 are:

The roots of the equation 5x^2 - 20x + 15 = 0 are:

Step 1: Identify the coefficients in the quadratic equation 5x^2 - 20x + 15 = 0. Here, a = 5, b = -20, and c = 15.
Step 2: Write down the quadratic formula: x = [ -b ± √(b² - 4ac) ] / (2a).
Step 3: Calculate b² - 4ac. First, find b²: (-20)² = 400. Then calculate 4ac: 4 * 5 * 15 = 300. Now, subtract: 400 - 300 = 100.
Step 4: Substitute the values into the quadratic formula: x = [20 ± √(100)] / (2 * 5).
Step 5: Calculate √(100), which is 10. Now the formula looks like this: x = [20 ± 10] / 10.
Step 6: Solve for the two possible values of x. First, calculate x = (20 + 10) / 10 = 30 / 10 = 3. Then calculate x = (20 - 10) / 10 = 10 / 10 = 1.
Step 7: The roots of the equation are x = 3 and x = 1.

Quadratic Equations – Understanding how to solve quadratic equations using the quadratic formula.
Discriminant – Recognizing the role of the discriminant in determining the nature of the roots.
Simplification – Properly simplifying expressions and ensuring accuracy in calculations.