Odpowiedź:
[tex]a)\\\\x^2+4x-21=0\\\\a=1\ \ ,\ \ b=4\ \ ,\ \ c=-21\\\\\Delta=b^2-4ac\\\\\Delta=4^2-4\cdot1\cdot(-21)=16+84=100\\\\\sqrt{\Delta}=\sqrt{100}=10\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-4-10}{2\cdot1}=\frac{-14}{2}=-7\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-4+10}{2\cdot1}=\frac{6}{2}=3[/tex]
[tex]b)\\\\\frac{9}{4}x^{2}-12x+16=0\\\\a=\frac{9}{4}\ \ ,\ \ b=-12\ \ ,\ \ c=16\\\\\Delta=b^2-4ac\\\\\Delta=(-12)^2-\not4\cdot\frac{9}{\not4}\cdot16=144-9\cdot16=144-144=0\\\\\sqrt{\Delta}=0\\\\x_{0}=-\dfrac{b}{2a}=-\dfrac{-12}{\not2^1\cdot\frac{9}{\not4_{2}}}=-\dfrac{-12}{\frac{9}{2}}=\not12^4\cdot\frac{2}{\not9_{3}}=\frac{8}{3}=2\frac{2}{3}[/tex]
[tex]c)\\\\-x^2+3\sqrt{2}x-5=0\ \ |\cdot(-1)\\\\x^2-3\sqrt{2}x+5=0\\\\a=1\ \ ,\ \ b=-3\sqrt{2}\ \ ,\ \ c=5\\\\\Delta=b^2-4ac\\\\\Delta=(-3\sqrt{2})^2-4\cdot1\cdot5=9\cdot2-20=18-20=-2\\\\\Delta<0\ \ r\'ownanie\ \ nie\ \ ma\ \ rozwiazania[/tex]
