Find the quadratic equation whose roots are 4+ √13 and 4– √13.
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Answer:
x² - 8x + 3 = 0
Step-by-step explanation:
α = 4 + √13 , β = 4 – √13
Sum of roots = 4 + √13 + 4 - √13
= 8
Product of roots = (4 + √13) (4 - √13)
[Formula: (a + b) (a - b) = a² - b²]
= (4)² - (√13)²
= 16 - 13
= 3
Equation:
x² - (sum of roots)x + product of roots = 0
x² - 8x + 3 = 0
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