Question

Найдите корни уравнений:
а) 3x^2-4x+1=0
б) 5x^2-10x-15=0
​

Answer 1

Ответ:

1) корни 2/6 и 1

2) корни -1 и 3

Решение:

1) D=16-4*3*1=16-12=4

x1= 4-2/6=2/6

x2= 4+2/6= 6/6=1

2) D=100-4*5*(-15) =100+300=400

x1= 10-20/10= -10/10=-1

x2=10+20/10= 30/10=3

Answer 2

а)

$3 {x}^{2} - 4x + 1 = 0 \\ D = {( - 4)}^{2} - 4 \times 3 \times 1 = 16 - 12 = 4 \\ \sqrt{D} = \sqrt{4} = 2 \\ x_1 = \frac{4 + 2}{2 \times 3} = \frac{6}{6} = 1 \\ x_2 = \frac{4 - 2}{2 \times 3} = \frac{2}{6} = \frac{1}{3}$

б)

$5 {x}^{2} - 10x - 15 = 0 \\ D = {( - 10)}^{2} - 4 \times 5 \times ( - 15) = 100 + 300 = 400 \\ \sqrt{D} = \sqrt{400} = 20 \\ x_1 = \frac{10 + 20}{2 \times 5} = \frac{30}{10} = 3 \\ x_2 = \frac{10 - 20}{2 \times 5} = \frac{ - 10}{10} = - 1$