If the roots of a quadratic equation are 1 + √5 and 1 - √5. The quadratic equation is?
- x² - 5x - 4 = 0
- x² - 2x + 4 = 0
- x² - 2x - 4 = 0
- None of these
Explanation
Given the roots are 1 + √5 and 1 - √5, we can find the quadratic equation using the sum and product of roots.
Step 1: Calculate the sum of roots
Sum of roots = (1 + √5) + (1 - √5) = 2
Step 2: Calculate the product of roots
Product of roots = (1 + √5)(1 - √5) = 1 - 5 = -4
Step 3: Form the quadratic equation
x² - (sum of roots)x + (product of roots) = 0
x² - 2x - 4 = 0
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