Task/28556417
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2.
2x² -3x+1 = 2x² -2x- x +1 =(2x² -2x ) - (x -1)= 2x(x -1) -(x-1) =(x-1)(2x-1) =
2(x-1)(x-1/2) .
* * * ax²+bx +c=a(x-x₁)(x-x₂) * * *
2x² -3x+1 =0 ; D =3² -4*2*1 =1 =1²;
x₁ =(3 +1)/(2*2) = 1 ;
x₂ =(3 -1)/4 =1/2 .
2x² -3x+1 =2(x-x₁)(x-x₂)=2(x-1)(x-1/2) .
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4.
7x² -3x -22 = 7x² -14x +11x -22 =7x(x-2) +11(x-2) = (x-2)(7x+11)=
7(x-2)(x+11/7) .
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7x² -3x -22 = 0 D =3² -4*7*(-22) =9 +616 =625 =25²
x₁ =(3 +25)/(2*7) = 2 ;
x₂ =(3 -25)/14 = -11/7 .
7x² -3x -22 =7(x-x₁)(x-x₂)=7(x-2)(x+11/7) .
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12.
7x² +3x -22 =7x² +14x -11x -22 =7x(x+2) -11(x+2) = (x+2)(7x-11)=
7(x+2)(x-11/7).
7x² +3x -22 = 0 см упр 4
x₁ =(-3 -25)/14 = -2 ;
x₂ =(-3 +25)/(2*7) = 11/7 .
7x² +3x -22 =7(x+2)(x-11/7).
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18.
x² - 4x +4 =(x -2)² = (x-2)(x-2) .
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x² - 4x +4 =0 D₁=2² -4 =0 * * * D = 4² -4*1*4 =0
x₁=x₂ =2 +0 =2
x² - 4x +4 =(x-x₁)(x-x₂)=(x-2)(x-2) .
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20.
x² - 6x +9 = (x-3)² = (x-3)(x-3) .
* * * x² - 3x -3x +9 =x(x-3) -3(x-3) =(x-3)(x-3) * * *
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x² - 6x +9 = 0 D =6² -4*1*9 =0 * * * D₁=(6/3)² -9 =9 -9 =0 * * *
x₁=x₂ =3 +0 =3 .
x² - 6x +9 =(x-x₁)(x-x₂) = (x-3)(x-3) .
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22.
-x²+2x +3 =- (x² -2x -3 ) = - (x² -3x +x -3 ) = -( x(x-3) +(x-3)) = -(x-3)(x+1).
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-x²+2x +3 = 0 ; D =2² -4*(-1)*3 =16 = 4²
x₁ =(-2 -4)/2*(-1) = 3 .
x₂ =(-2 +4)/(-2) = - 1.
-x²+2x +3 = -1(x -3) (x -(-1) ) =- (x-3)(x+1) . * * * (3-x)(x+1) * * *