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How many solutions are there to the equation 5x^2−6x+8=0?
3 Answers
- la consoleLv 71 day agoFavorite Answer
5x² - 6x + 8 = 0
5x² - 6x = - 8
x² - (6/5).x = - 8/5
x² - (6/5).x + (3/5)² = - (8/5) + (3/5)²
x² - (6/5).x + (3/5)² = - (40/25) + (9/25)
[x - (3/5)]² = - 31/25 ← no possible because a square is always positive or zero
To go further, with complex numbers
[x - (3/5)]² = - 31/25
[x - (3/5)]² = i².(31/25)
x - (3/5) = ± i.(√31)/5
x = (3/5) ± [i.(√31)/5]
x = (3 ± i.√31)/5
x₁ = (3 + i.√31)/5
x₂ = (3 - i.√31)/5
- ?Lv 724 hours ago
5x^2 − 6x + 8 = 0
Complex solutions:
x = 1/5 (3 - i sqrt(31))
x = 1/5 (3 + i sqrt(31))
