5.10. a) -x² - 5x + 14 = 0; 6) -3x² - 2x + 5 = 0; в) -x² + 26x - 25 = 0; г) -5x² - 9x + 2 = 0.

Решение:

1. 5.10. а) -x² - 5x + 14 = 0




• \( a = -1, b = -5, c = 14 \)


• \( D = b^2 - 4ac = (-5)^2 - 4 · (-1) · 14 = 25 + 56 = 81 \)


• \( \sqrt{D} = 9 \)


• \( x_1 = \frac{-(-5) + 9}{2 · (-1)} = \frac{5 + 9}{-2} = \frac{14}{-2} = -7 \)


• \( x_2 = \frac{-(-5) - 9}{2 · (-1)} = \frac{5 - 9}{-2} = \frac{-4}{-2} = 2 \)




2. 5.10. б) -3x² - 2x + 5 = 0




• \( a = -3, b = -2, c = 5 \)


• \( D = b^2 - 4ac = (-2)^2 - 4 · (-3) · 5 = 4 + 60 = 64 \)


• \( \sqrt{D} = 8 \)


• \( x_1 = \frac{-(-2) + 8}{2 · (-3)} = \frac{2 + 8}{-6} = \frac{10}{-6} = -\frac{5}{3} \)


• \( x_2 = \frac{-(-2) - 8}{2 · (-3)} = \frac{2 - 8}{-6} = \frac{-6}{-6} = 1 \)




3. 5.10. в) -x² + 26x - 25 = 0




• \( a = -1, b = 26, c = -25 \)


• \( D = b^2 - 4ac = 26^2 - 4 · (-1) · (-25) = 676 - 100 = 576 \)


• \( \sqrt{D} = 24 \)


• \( x_1 = \frac{-26 + 24}{2 · (-1)} = \frac{-2}{-2} = 1 \)


• \( x_2 = \frac{-26 - 24}{2 · (-1)} = \frac{-50}{-2} = 25 \)




4. 5.10. г) -5x² - 9x + 2 = 0




• \( a = -5, b = -9, c = 2 \)


• \( D = b^2 - 4ac = (-9)^2 - 4 · (-5) · 2 = 81 + 40 = 121 \)


• \( \sqrt{D} = 11 \)


• \( x_1 = \frac{-(-9) + 11}{2 · (-5)} = \frac{9 + 11}{-10} = \frac{20}{-10} = -2 \)


• \( x_2 = \frac{-(-9) - 11}{2 · (-5)} = \frac{9 - 11}{-10} = \frac{-2}{-10} = \frac{1}{5} \)

Ответ: а) \( x_1 = -7, x_2 = 2 \); б) \( x_1 = -\frac{5}{3}, x_2 = 1 \); в) \( x_1 = 1, x_2 = 25 \); г) \( x_1 = -2, x_2 = \frac{1}{5} \).