Разложить на множители:
1)х^2-17x+60
2)3x^2+35x-38
3)2x^2-297x+295
4)x^2+26x+105
помогите пожалуйста.
Ответы на вопрос
Ответил paradiseva
0
Разложение квадратного трёхчлена выглядит следующим образом:
============ 1 ============
![x^2-17x+60=0\
D = (-17)^2-4*1*60=289-240=49\
x_1= frac{17+7}{2} = frac{24}{2}=12\
x_2= frac{17-7}{2} = frac{10}{2}=5\
x^2-17x+60=(x-12)(x-5)](https://tex.z-dn.net/?f=x%5E2-17x%2B60%3D0%5C%0AD+%3D+%28-17%29%5E2-4%2A1%2A60%3D289-240%3D49%5C%0Ax_1%3D+frac%7B17%2B7%7D%7B2%7D+%3D++frac%7B24%7D%7B2%7D%3D12%5C%0Ax_2%3D+frac%7B17-7%7D%7B2%7D+%3D++frac%7B10%7D%7B2%7D%3D5%5C%0Ax%5E2-17x%2B60%3D%28x-12%29%28x-5%29 "x^2-17x+60=0\
D = (-17)^2-4*1*60=289-240=49\
x_1= frac{17+7}{2} = frac{24}{2}=12\
x_2= frac{17-7}{2} = frac{10}{2}=5\
x^2-17x+60=(x-12)(x-5)")
============ 2 ============
![3x^2+35x-38=0\
D=35^2-4*3*(-38)=1225+456=1681\
x_1= frac{-35+41}{6}=1\
x_2= frac{-35-41}{6}= -frac{76}{6} =- frac{38}{3} \
3x^2+35x-38=3(x-1)(x+frac{38}{3})](https://tex.z-dn.net/?f=3x%5E2%2B35x-38%3D0%5C%0AD%3D35%5E2-4%2A3%2A%28-38%29%3D1225%2B456%3D1681%5C%0Ax_1%3D+frac%7B-35%2B41%7D%7B6%7D%3D1%5C%0Ax_2%3D+frac%7B-35-41%7D%7B6%7D%3D+-frac%7B76%7D%7B6%7D+%3D-+frac%7B38%7D%7B3%7D+%5C%0A3x%5E2%2B35x-38%3D3%28x-1%29%28x%2Bfrac%7B38%7D%7B3%7D%29 "3x^2+35x-38=0\
D=35^2-4*3*(-38)=1225+456=1681\
x_1= frac{-35+41}{6}=1\
x_2= frac{-35-41}{6}= -frac{76}{6} =- frac{38}{3} \
3x^2+35x-38=3(x-1)(x+frac{38}{3})")
============ 3 ============
![2x^2-297x+295=0\
D=(-297)^2-4*2*295=88209-2360=85849\
x_1= frac{297+293}{4} = 147.5\
x_2= frac{297-293}{4} = 1\
2x^2-297x+295=2(x-147.5)(x-1)](https://tex.z-dn.net/?f=2x%5E2-297x%2B295%3D0%5C%0AD%3D%28-297%29%5E2-4%2A2%2A295%3D88209-2360%3D85849%5C%0Ax_1%3D+frac%7B297%2B293%7D%7B4%7D+%3D+147.5%5C%0Ax_2%3D+frac%7B297-293%7D%7B4%7D+%3D+1%5C%0A2x%5E2-297x%2B295%3D2%28x-147.5%29%28x-1%29 "2x^2-297x+295=0\
D=(-297)^2-4*2*295=88209-2360=85849\
x_1= frac{297+293}{4} = 147.5\
x_2= frac{297-293}{4} = 1\
2x^2-297x+295=2(x-147.5)(x-1)")
============ 4 ============
![x^2+26x+105=0\
D=26^2-4*1*105=676-420=256\
x_1= frac{-26+16}{2}= -5\
x_2= frac{-26-16}{2}= -21\
x^2+26x+105=(x+5)(x+21)](https://tex.z-dn.net/?f=x%5E2%2B26x%2B105%3D0%5C%0AD%3D26%5E2-4%2A1%2A105%3D676-420%3D256%5C%0Ax_1%3D+frac%7B-26%2B16%7D%7B2%7D%3D+-5%5C%0Ax_2%3D+frac%7B-26-16%7D%7B2%7D%3D+-21%5C%0Ax%5E2%2B26x%2B105%3D%28x%2B5%29%28x%2B21%29%0A "x^2+26x+105=0\
D=26^2-4*1*105=676-420=256\
x_1= frac{-26+16}{2}= -5\
x_2= frac{-26-16}{2}= -21\
x^2+26x+105=(x+5)(x+21)")
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