Answer:
1. x = ±9
2. [tex]x=\pm \sqrt{13}[/tex]
3. 12 and -12.
4. Antoine is incorrect. There exists two solutions x=5 and x= -5.
Step-by-step explanation:
According to the questions,
Problem 1. [tex]x^{2}-81=0[/tex] i.e. [tex]x^{2}=81[/tex] i.e. x = ±9.
Problem 2. [tex]2x^{2}-26=0[/tex] i.e. [tex]x^{2}-13=0[/tex] i.e. [tex]x^{2}=13[/tex] i.e. [tex]x=\pm \sqrt{13}[/tex]
Problem 3. [tex]f(x)=x^{2}-144[tex]
To find the roots, we take, [tex]x^{2}-144=0[tex] i.e. [tex]x^{2}=144[tex] i.e. x = ±12.
Thus, the options are 12 and -12.
Problem 4. We have [tex]f(x)=x^{2}+25[tex]
For the roots, we take, [tex]x^{2}+25=0[tex] i.e. [tex]x^{2}=25[tex] i.e. x = ±5.
Thus, Antoine is not correct and two solutions namely x=5 and x= -5 exists.
