Question

Daję naj!!!!!!!!!!!!​

Answer 1

a)

[tex]-x^2+x+2\geq 0\\\Delta=1^2-4*(-1)*2=1+8=9\\\sqrt\Delta=3\\x_1=\frac{-1-3}{2*(-1)}=\frac{-4}{-2}=2\\x_2=\frac{-1+3}{2*(-1)}=\frac{2}{-2}=-1\\x\in\left < -1,2\right >[/tex]

b)

[tex]3x^2+10x+3=0\\\Delta=10^2-4*3*3=100-36=64\\\sqrt\Delta=8\\x_1=\frac{-10-8}{2*3}=\frac{-18}{6}=-3\\x_2=\frac{-10+8}{2*3}=\frac{-2}{6}=-\frac{1}{3}\\x\in\{-3,-\frac{1}{3}\}[/tex]

c)

[tex]2x^2+5x-3 < 0\\\Delta=5^2-4*2*(-3)=25+24=49\\\sqrt\Delta=7\\x_1=\frac{-5-7}{2*2}=\frac{-12}{4}=-3\\x_2=\frac{-5+7}{2*2}=\frac{2}{4}=\frac{1}{2}\\x\in(-3,\frac{1}{2})[/tex]

d)

[tex]-x^2-x-1 > 0\\\Delta=(-1)^2-4*(-1)*(-1)=1-4=-3 < 0\\x\in\oslash[/tex]