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pavelpdr23
@pavelpdr23
August 2022
1
18
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Разложить квадратный трехчлен на множители:
а) [tex] x^{2} [/tex]- 7х + 10
б) 7[tex] x^{2} [/tex] + 20х - 3
в) 12[tex] x^{2} [/tex] - 588
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oganesbagoyan
Verified answer
task/26474004
--------------------
Разложить квадратный трехчлен на множители:
а) x
²
- 7x + 10
б) 7x
²
+ 20x - 3
в) 12x
²
- 588
* * * ax
²+bx +c =a(x -x₁)(x-x
₂) * * *
а)
x² - 7x + 10 =x² - 7x + 10 = (x² - 2x) -(5x +10 ) =x(x-2) -5(x-2) =(x-2)(x-5).
* * *
x² -7x +10 =0 ; D =7² - 4*1*10 = 49 - 40 =9 =3²
x₁ =(7-3)/2*1 =4/2=2;
x
₂=(7+3)/2 =5 . (x -2)(x-5)
* * *
б)
7x² + 20x - 3 =7(x +3)(x - 1/7) || (x +3)(7x - 1) ||
* * *
7x² +20x -3=0 ; D₁ =10² - 7*(-3) = 100+21=121=11²
x₁ =(-10 -11) /7 =-21/7 = -3 ;
x₂=(-10 +11) /7 = 1/7. (x -(-3)) (x -1/7) =7(x+3)(x -1/7) = (x+3)(7x -1).
--------
в)
12x² - 588 =12(x² - 49)=12(x² - 7²) =12(x - 7) (x + 7) .
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Answers & Comments
Verified answer
task/26474004--------------------
Разложить квадратный трехчлен на множители:
а) x² - 7x + 10
б) 7x² + 20x - 3
в) 12x² - 588
* * * ax²+bx +c =a(x -x₁)(x-x₂) * * *
а) x² - 7x + 10 =x² - 7x + 10 = (x² - 2x) -(5x +10 ) =x(x-2) -5(x-2) =(x-2)(x-5).
* * *
x² -7x +10 =0 ; D =7² - 4*1*10 = 49 - 40 =9 =3²
x₁ =(7-3)/2*1 =4/2=2;
x₂=(7+3)/2 =5 . (x -2)(x-5)
* * *
б) 7x² + 20x - 3 =7(x +3)(x - 1/7) || (x +3)(7x - 1) ||
* * *
7x² +20x -3=0 ; D₁ =10² - 7*(-3) = 100+21=121=11²
x₁ =(-10 -11) /7 =-21/7 = -3 ;
x₂=(-10 +11) /7 = 1/7. (x -(-3)) (x -1/7) =7(x+3)(x -1/7) = (x+3)(7x -1).
--------
в) 12x² - 588 =12(x² - 49)=12(x² - 7²) =12(x - 7) (x + 7) .