Общий вид квадратного уравнения:
ax² + bx + c = 0
через D₁).
3x² + 22x - 16 = 0
a = 3, b = 22, c = - 16,
k = b/2 =
= 22/2 = 11
D₁ = k² - ac = 11² - 3 · ( -16 )
= 121 + 48 = 169 = 13²
x₁,₂ = ( -k ± √D₁)/a = ( -11 ± √13² )/3 =
= ( -11 ± 13 )/3
x₁ = ( -11 - 13 )/3 = - 24/3 = -8
x₂ = ( -11 + 13 )/3 = 2/3
через D).
3x² + 22x - 16 = 0
a = 3, b = 22 , c = - 16
D = b² - 4ac = 22² - 4 · 3 · ( -16 ) =
= 484 + 192 = 676 = 26²
x₁,₂ = ( -b ± √D )/2a = ( -22 ± √26² )/2 · 3 =
= ( -22 ± 26 )/6
x₁ = ( -22 - 26 )/6 = - 48/6 = -8
x₂ = ( -22 + 26)/6 = 4/6 = 2/3
ответ: -8; 2/3.
1<-х<2 и меняем знак!
-1>x>-2