Answer: x²-11x+18=0
Step-by-step explanation:
[tex]x_1=2\ \ \ \ x_2=9\ \ \ \ x^2+bx+c=0\ ?[/tex]
According to the Vieta theorem:
[tex]\displaystyle\\\left \{ {{x_1+x_2=-b} \atop {x_1*x_2=c}} \right.\ \ \ \ \left \{ {{2+9=-b} \atop {2*9=c}} \right. \ \ \ \ \left \{ {{11=-b\ \ \ \ (1)} \atop {18=c\ \ \ \ \ (2)}} \right. \\[/tex]
Multiply both sides of equation (1) by -1:
[tex]\displaystyle\\\left \{ {{-11=b} \atop {18=c}} \right. \\Hence,\\x^2-11x+18=0[/tex]
