Разложите на множители 1)-х^2+4х-3; 2)х^2+4х+3. Created by Tvoibol. matematika-ru

Разложите на множители 1)-х^2+4х-3; 2)х^2+4х+3...

coolpandaRF

$-x^{2}+4x-3=-x^{2}+3x+x-3=-x(x-3)+(x-3)=(x-3)(-x+1)=(x-3)(1-x)$

$x^{2}+4x+3=x^{2}+3x+x+3=x(x+3)+(x+3)=(x+3)(x+1)$

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2407Alexa

ax²+bx+c=a(x-x1)(x-x2).

1) -x²+4x-3=-(x-3)(x-1)=(3-x)(x-1)=3x-3-x²+x=-x²+4x-3.

D=(-4)²-4×(-1)×(-3)=16-12=4

x1=(-4-√4)/2×(-1)=(-4-2)/(-2)=(-6)/(-2)=3

x2=(-4+√4)/2×(-1)=(-4+2)/(-2)=(-2)/(-2)=1

2) x²+4x+3=(x-(-3))(x-(-1))=(x+3)(x+1)=x²+x+3x+3=x²+4x+3.

D=(-4)²-4×1×3=16-12=4

x1=(-4-√4)/2×1=(-4-2)/2=(-6)/2=-3

x2=(-4+√4)/2×1=(-4+2)/2=(-2)/2=-1

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