a, Để F(x) có nghiệm thì F(x) = 0
⇔ 2x - 4 = 0
⇔ 2(x - 2) = 0
⇔ x - 2 = 0
⇔ x = 2
Vậy F(x) có nghiệm là 2.
b, Ta có: G(x)=F(x)+x²-x+6
⇔ G(x) = 2x - 4 + x² - x + 6
⇔ G(x) = x² + x + 2
⇔ G(x) = x² + 2.x.$\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{7}{4}$
⇔ G(x) = (x + $\frac{1}{2}$)² + $\frac{7}{4}$ = 0
⇔ G(x) = (x + $\frac{1}{2}$)² = -$\frac{7}{4}$
Vì (x + $\frac{1}{2}$)² ≥ 0 mà (x + $\frac{1}{2}$)² = -$\frac{7}{4}$ (vô lí)
⇒ G(x) vô nghiệm
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