Question

Fie polinomul $x^{4}-12 x^{2} + 35$ f . Aratati ca polinomul f nu are radacini intregi

Answer 1

fie  x²=    y ,  y≥0 
ecuatia  devine
y²-12y+35=0
Δ=144-120=4
y1=(12-√4)/2=5  x1, 2=+/-√5  ∉Z
y2=(12+2)/2=7  y2;3=+/-√7 ∈Z