Решите уравнения: 1)3x^2+10x+7=0 2)-7x^2-4x+11=0 3)-23x^2-22x-1=0 4)3x^2-14x+16=0

Решим уравнения через дискриминант.

1) 3x^2 + 10x + 7 = 0.

a = 3; b = 10; c = 7;

D = b^2 - 4ac; D = 10^2 - 4 * 3 * 7 = 100 - 84 = 16 (√D = 4);

x = (-b ± √D)/2a;

х₁ = (-10 + 4)/(3 * 2) = (-6)/6 = -1;

х₂ = (-10 - 4)/6 = (-14)/6 = -2 2/6 = -2 1/3.

2) -7x^2 - 4x + 11 = 0.

a = -7; b = -4; c = 11;

D = b^2 - 4ac; D = (-4)^2 - 4 * (-7) * 11 = 16 + 308 = 324 (√D = 18);

x = (-b ± √D)/2a;

х₁ = (4 + 18)/(-7 * 2) = 22/(-14) = -1 8/14 = -1 4/7;

х₂ = (4 - 18)/(-14) = (-14)/(-14) = 1.

3) -23x^2 - 22x - 1 = 0.

a = -23; b = -22; c = -1;

D = b^2 - 4ac; D = (-22)^2 - 4 * (-23) * (-1) = 484 - 92 = 392 (√D = √392 =14√2);

x = (-b ± √D)/2a;

х₁ = (22 + 14√2)/(-23 * 2) = (22 + 14√2)/(-46) = - (11 + 7√2)/23;

х₂ = - (11 - 7√2)/23.

4) 3x^2 - 14x + 16 = 0.

a = 3; b = -14; c = 16;

D = b^2 - 4ac; D = (-14)^2 - 4 * 3 * 16 = 196 - 192 = 4 (√D = 2);

x = (-b ± √D)/2a;

х₁ = (14 + 2)/(3 * 2) = 16/6 = 2 2/6 = 2 1/3;

х₂ = (14 - 2)/6 = 12/6 = 2.