Question

Write an absolute value equation that has the solutions x=2 and x=9 please help

Answer 1

Answer: x²-11x+18=0

Explanation:

`x_1=2\ \ \ \ x_2=9\ \ \ \ x^2+bx+c=0\ ?`

According to the Vieta theorem:

`\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. \\`

Multiply both sides of equation (1) by -1:

`\displaystyle\\\left \{ {{-11=b} \atop {18=c}} \right. \\Hence,\\x^2-11x+18=0`