Найдите сумму и произведение корней каждого из данных уравнений: 3x²+4x-6=0 -x²-7x+8=0 2x²-5x+1=0 5x²2+x-4=0

Решим уравнение и найдем сумму и произведение его корней:

1) 3х^2 + 4х - 6 = 0;

D = b^2 - 4ac = 16 + 4 * 3 * 6 = 16 + 72 = 88;

x1 = (-b + √D)/2a = (-4 + 4√22)/6 = - 2/3 + 2√22/3;

x2 = (-b - √D)/2a = (-4 - 4√22)/6 = - 2/3 - 2√22/3;

x1 + x2 = -2/3 + 2√22/3 - 2/3 - 2√22/3 = -4/3 = -1 1/3.

x1 * x2 = (-2/3 + 2√22/3) * (-2/3 - 2√22/3) = 4/9 - 4 * 22/9 = 4/9 - 88/9 = -84/9 = -9 1/3.

2) D = 49 - 4 * 8 = 49 - 32 = 17;

x1 = (7 + √17)/2 = 7/2 + √17/2;

x2 = (7 - √17)/2 = 7/2 - √17/2;

x1 + x2 = 7/2 + √17/2 + 7/2 - √17/2 = 14/2 = 7;

x1 * x2 = (7/2 + √17/2) * (7/2 - √17/2) = 49/4 - 17/4 = 32/4 = 8.

3) D = 25 - 8 = 17;

x1 = (-5 + √17)/4 = -5/4 + √17/4;

x2 = (-5 - √17)/4 = -5/4 - √17/4;

x1 + x2 = -5/4 + √17/4 -5/4 - √17/4 = -10/4 = -2 1/2;

x1 * x2 = (-5/4 + √17/4) * (-5/4 - √17/4) = 25/16 - 17/16 = 8/16 = 1/2.

4) D = 1 + 120 = 121;

x1 = (-1 + 11)/10 = 1;

x2 = (-1 - 11)/10 = -12/10 = -1,2;

x1 + x2 = 1 - 1,2 = -0,2;

x1 * x2 = 1 * (-1,2) = -1,2.