Answer:
Step-by-step explanation:
1) x² - x + 2 ≤ 0
x² -x - x + 2 ≤0
x(x - 1) - (x - 1) ≤ 0
(x - 1)(x - 1) ≤0
No solution
3) x² + 9x + 18 < 0
x² + 6x + 3x + 18 < 0
x(x + 6) +3(x + 6) < 0
(x + 6)(x + 3) < 0
x > - 6; x < -3
-6 < x < -3
4) m² - 7m - 10 < 0
a = 1 ; b = -7 c = -10
D = b² - 4ac = (-7)² - 4*1*(-10) = 49 + 40 = 89
[tex]m=\dfrac{-b+\sqrt{D}}{2a} ; m = \dfrac{-b-sqrt{D}}{2a}\\\\\\m=\dfrac{-(-7)+\sqrt{89}}{2*1} \ ; \ m=\dfrac{-(-7)-\sqrt{89}}{2*1}\\\\\\m=\dfrac{7+9.43}{2} \ ; \ m=\dfrac{7-9.43}{2}\\\\m=\dfrac{16.43}{2} \ ; \ m=\dfrac{-2.43}{2}\\\\m=8.22 ; m = -1.21[/tex]
-1.21 < m < 8.22
-1 < m < 8
5) 2x² - 3x - 14 < 0
2x² + 4x - 7x - 14 < 0
2x(x + 2) - 7(x + 2) < 0
(x + 2)(2x -7) < 0
-2 < x < 7/2
-2 < x < 3.5
