Question

Simplificati E(x)

E(x)=18x² -3x-10 totul supra 9x²+12x+4 

Answer 1

$E(x)= \frac{18x^2-3x-10}{9x^2+12x+4}$

[tex]18x^2-3x-10=0 a=18 b=-3 c=-10 delta=b^2-4ac= (-3)^2-4*18*(-10)=9+720=729 [/tex]

$x1= \frac{3+27}{36}= \frac{30}{36}= \frac{10}{12} = \frac{5}{6}$

$x2= \frac{3-27}{36}= \frac{-24}{36}= \frac{-8}{12}= \frac{-4}{6}= \frac{-2}{3}$

Conform formulei : a(x-x1)(x-x2) vom avea : $18(x- \frac{5}{6})(x+ \frac{2}{3})$ =>>>$(6x-5)(3x+2)$



 [tex]9x^2+12x+4=0 a=9 b=12 c=4 delta=b^2-4ac = 12^2-4*9*4=144-144=0[/tex]

Cand delta=0 vom avea o radacina

$x1= \frac{-12+0}{18}= \frac{-12}{18}= \frac{2}{3}$

a(x-x1)=$9(x- \frac{2}{3})$=>>>> 9(x-2)

$E(x)= \frac{(6x-5)(3x+2)}{9*(x-2)}$