Question

Descompune in factori!!..ms
-x^{2} +2x+9

Answer 1

aflam radacinile ecuuatiei atasate

x1.2=(-2+-√(4+36))/(-2)=(-2+-2√10)/(-2)=1+-√10
a(x-x1)(x-x2)cu a=-1,  va fi

-(x-1+√10)(x-1-√10)
sau dac vrei far "- "in fata
(x-1+√10)(1+√10-x)

verificare
-(x-1+√10)(x-1-√10)=
-((x-1)²-10)=-(x²-2x+1-10)=-(x²-2x-9)=-x²+2x+9, bine descompus
 
extra
descompunereab unei expresiide grad2 in 2 factoride grad1 este unica


ALTFEL ,mai ca la gimnaziu

-x²+2x+9=-x²+2x-1+10=-(x²-2x+1)+10=-(x-1)²+10=10-(x-1)²= (√10)²-(x-1)²=
(√10-x+1)(√10+x-1)

Answer 2

[tex]\it -x^2+2x+9 = -(x^2-2x-9) = -(x^2-2x+1-10) = \\\;\\ = -[(x-1)^2-(\sqrt{10})^2] = -(x-1-\sqrt{10})(x-1+\sqrt{10})[/tex]