Question

Someone please help me I’m struggling

Answer 1

Answer:
`x =\frac{\fbox{-3}+i \sqrt{} \fbox{11} }{\fbox{10}}\: \: \: \: or\: \: \: \: x =\frac{\fbox{-3}-i\sqrt{} \fbox{11} }{\fbox{10}}`

Explanation:

Find the discriminant.

-5x² - 3x - 1 = 0

D = b² - 4a · c

a = - 5

b = - 3

c = - 1

`D=(-3)^(2) -4 \cdot (-5) \cdot (-1) = -11 < 0\\\\D=-11=- 1 \cdot 11 = i^(2) \cdot 11\\\\√(D) =\sqrt{i^(2) \cdot 11} =i√(11)\\\\ x_(1) =(3+i√(11) )/(2 \cdot (- 5)) =(3+i√(11) )/(-10)=(-3-i√(11) )/(10)\\\\x_(2) =(3-i√(11) )/(2 \cdot (- 5)) =(3-i√(11) )/(-10)=(-3+i√(11) )/(10)`