[tex]a) \ x^{2}+ax+3\\\\dla \ \ x = 2 \ jest \ rowna \ 1\\\\2^{2}+a\cdot2 + 3 = 1\\\\4 + 2a+3 = 1\\\\2a+7 = 1\\\\2a=1-7\\\\2a = -6 \ /:2\\\\\boxed{a = -3}[/tex]
[tex]b) \ -2x^{5}+4x^{4}+ax\\\\dla \ \ x = -1 \ jest \ rowna \ 3\\\\-2\cdot(-1)^{5}+4\cdot(-1)^{4}+a\cdot(-1) = 3\\\\-2\cdot(-1) + 4\cdot1+a\cdot(-1) = 3\\\\2+4-a= 3\\\\-a+6 = 3\\\\-a = 3-6\\\\-a = -3 \ \ /:(-1)\\\\\boxed{a = 3}[/tex]
[tex]c) \ \frac{1}{2}x^{5}+ax^{3}-3\\\\dla \ \ x =-2 \ jest \ rowna \ 5\\\\\frac{1}{2}\cdot(-2)^{5}+a\cdot(-2)^{3}-3 = 5\\\\\frac{1}{2}\cdot(-32)+a\cdot(-8)-3 = 5\\\\-16-8a-3 = 5\\\\-8a-19 = 5\\\\-8a = 5+19\\\\-8a = 24 \ \ /:(-8)\\\\\boxed{a = -3}[/tex]
[tex]d) \ 9x^{3}+ax^{2}-6x\\\\dla \ \ x = -\frac{1}{5} \ jest \ rowna \ 1\\\\9\cdot(-\frac{1}{5})^{3} + a\cdot(-\frac{1}{5})^{2} -6\cdot(-\frac{1}{5}) = 1\\\\9\cdot(-\frac{1}{125})+a\cdot\frac{1}{25}+6\cdot\frac{1}{5} = 1 \ \ /\cdot125 \\\\-9+5a+150 = 125\\\\5a + 141 = 125\\\\5a = 125-141\\\\5a = -16 \ \ /:5\\\\a = -\frac{16}{5}\\\\\boxed{a = -3\frac{1}{5}}[/tex]
