Rownanie kwadratowe ma 1 pierwiastek wtedy, kiedy [tex]\Delta = 0[/tex]
[tex]x_0=\frac{-b}{2a}[/tex]
[tex]x^2-(a+2)x+(a+10)=0\\\\a=1\\b=-(a+2)=-a-2\\c=a+10\\\\\Delta=b^2-4ac\\\Delta=(-a-2)^2-4*1*(a+10)\\\Delta=a^2+4a+4-4(a+10)\\\Delta=a^2+4a+4-4a-40\\\Delta=a^2-36\\a^2-36=0\\a^2=36\\a=6, a=-6\\\\\text{Dla a=6}\\a=1\\b=-6-2=-8\\c=6+10=16\\\\x_0=\frac{-(-8)}2=\frac82=4\\\\\text{Dla a=-6}\\a=1\\b=-(-6)-2=6-2=4\\c=-6+10=4\\\\x_{0}=\frac{-4}2=-2[/tex]
Odp. Dla parametru a=6, rownanie ma pierwiatek x0=4, a dla parametru a=-6, rownanie ma pierwiastek x0=-2