Question

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Answer 1

Answer:

Step-by-step explanation:

1) x² + 3x + 1 = 0

a = 1    b = 3     c = 1

=> Δ = b² - 4ac = 9 - 4.1.1 = 5 > 0

so the quadratic equation have 2 solutions

=> x = $\frac{-3+\sqrt{5} }{4}$

or  x = $\frac{-3-\sqrt{5} }{4}$

2) x² + 4x - 8 = 0

a = 1    b' = 2    c = -8

Δ' = b'² - ac = 4 - 1.(-8) = 12 > 0

so the quadratic equation have 2 solutions

=> x = $\frac{-2+\sqrt{12} }{1}=-2+\sqrt{12}$

or x = $-2-\sqrt{12}$

3) x² - 5x -12 = 0

a = 1       b = -5    c = -12

Δ = b² - 4ac = 25 - 4.1.(-12) = 25 + 48 = 73 > 0

so the quadratic equation have 2 solutions

=> x = $\frac{5+\sqrt{73} }{2}$

or x = $\frac{5-\sqrt{73} }{2}$