Question

Cum se descompune 2x^2-7x-17?

Answer 1

Observam ca aici avem forma ecuatiei de grad ll :
ax²+bx+c=0, a≠0
Ecuatia de acest tip se descompune in factori, si are mereu forma:
ax²+bx+c=a(x-x1)(x-x2)
unde x1 si x2 sunt solutiile a ecuatiei de grad ll

Adica rezolvam ecuatia, si aflam solutiile ei:
2x²-7x-17=0
a=2
b=-7
c=-17
∆=b²-4ac
∆= (-7)²-4*2*(-17)=49+136=185
x1,2= (-b±√∆ )/2a
x1,2=(-(-7)±√185)/2*2= (7±√185)/4

x1=(7+√185)/4
x2=(7-√185)/4

Descompunem in factori:
a(x-x1)(x-x2)= 2[x- (7+√185)/4][x-(7-√185)/4]