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True [87]
3 years ago
15

Find the roots of the equation x^2+2x+5=0

Mathematics
1 answer:
stiv31 [10]3 years ago
7 0

Answer:

x = - 1 ± 2i

Step-by-step explanation:

we can use the discriminant b² - 4ac to determine the nature of the roots

• If b² - 4ac > , roots are real and distinct

• If b² - 4ac = 0, roots are real and equal

• If b² - ac < 0, roots are not real

for x² + 2x + 5 = 0

with a = 1, b = 2 and c = 5, then

b² - 4ac = 2² - (4 × 1 × 5 ) = 4 - 20 = - 16

since b² - 4ac < 0 there are 2 complex roots

using the quadratic formula to calculate the roots

x = ( - 2 ± \sqrt{-16} ) / 2

  = (- 2 ± 4i ) / 2 = - 1 ± 2i


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