Question

descompuneti in factori trinomul 4x2-4x-21

Answer 1

4x²-4x-21=
4x²-4x+1-22=(2x-1)²-22=(2x-1)²-√22²=(2x-1-√22)(2x-1+√22)

verificare cu clasa a 9-a
ax²+bx+c=a(x-x1) (x-x2)
 a=4
b=-4
c=-21
4x²-4x-21=4(x-x1) (x-x2)
x1,2= {4+-√(16+16*21)]/2*4=( 4+-4√22)/8= (1+-√22)/2

4 (x-(1+√22)/2) (x--(1-√22))/2= (2x-1-√22)(2x-1+√22)


Verificare cu suma si produs
x1+x2= -b/a= -(-4)/4=1
 (1-√22+1+√22)/2=2/2=1
x1*x1= (1-√22²)/4=-21/4=c/a
problema este bine rezolvata