Odpowiedź:
2 x² - (m -1) x + m+ 1 = 0
Musi być :
Δ > 0 i x1*x2 > 0
Δ = ( m-1)² -4*2*( m +1) = m² -2 m + 1 - 8 m - 8 = m² - 10 m - 7
Δm = 100 - 4*1*(-7) = 128 = 64*2 > 0
√Δ = 8√2
m1 = [tex]\frac{10 - 8\sqrt{2} }{2}[/tex] = 5 - √2 m2 = 5 + √2
I. m ∈ ( -∞ ; 5 - √2 ) ∪ ( 5 + √2 ; +∞)
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II . x1*x2 = [tex]\frac{c}{a}[/tex] = [tex]\frac{ m + 1}{2}[/tex] > 0 ⇔ m + 1 > 0 ⇔ m > -1
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Z I. i II. ⇒ m ∈ ( - 1; 5 - √2) ∪ ( 5 + √2 ; +∞ )
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Szczegółowe wyjaśnienie:
