Question

Решите объведённые номера.

Answer 1

$1) \ 3x {}^{2} - x = 0 \\ x(3x - 1) = 0 \\ x = 0 \\ or \\ 3x - 1 = 0 \\ 3x = 1 \\ x = \dfrac{1}{3} .$

$2) \ 5x {}^{2} - 12x - 65 = 0 \\ D = ( - 12) {}^{2} - 4 \times 5 \times ( - 65) = 144 + 1300 = 1444 \\ x_{1/2} = \displaystyle \frac{12 \pm38}{10} \\ \\ x_{1} = \frac{12 - 38}{10} = \frac{ - 26}{10} = - 2.6 \\ \\ x_{2} = \frac{12 + 38}{10} = \frac{50}{10} = 5.$

$3) \ - 3x {}^{2} - 24x - 49 = 0 \\ 3x {}^{2} + 24x + 49 = 0 \\ D = 24 {}^{2} - 4 \times 3 \times 49 = 576 - 588 = - 12 \\ D < 0 \rightarrow \: x \in \: \varnothing.$

Answer 2

3х²-х=0

х*(3х-1)=0

1)х=0

2)3х-1=0; 3х=1; х=1/3.

ответ: 0 и 1/3.

5х²-12х-65=0

а=5;b=-12;c=-65

D=b²-4ac=(-12)²-4*5*(-65)=144+1300=1444

x_{1;2}=(-b±√D)/(2a)

x_1=(-(-12)-√1444)/(2*5)=(12-38)/10=-26/10=-13/5=-2 3/5=-2,6

x_2=(12+38)/10=50/10=5

ответ: -2,6 и 5.

-3х²-24х-49=0

а=3;b=-24;c=-49

D=b²-4ac=(-24)²-4*3*(-49)=576-588=-12

D<0 → корней нет.