Question

zadanie w związku c)​

Answer 1

Verified answer

c)

[tex]2x^{2}-7x-4 \leq 0\\\\a = 2, \ b = -7, \ c = -4\\\\\Delta = b^{2}-4ac = (-7)^{2}-4\cdot2\cdot(-4) = 49 + 32 = 81\\\\\sqrt{\Delta} = \sqrt{81} = 9\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{7-9}{2\cdot2} = \frac{-2}{4} = -\frac{1}{2}\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{7+9}{4} = \frac{16}{4} = 4[/tex]

a > 0, to ramiona paraboli skierowane do góry, więc wartości ≤ 0 znajdują się pod osią OX

[tex]\boxed{x \in\langle-\frac{1}{2}; 4\rangle}[/tex]