Question

Can you help me with my work

Answer 1

Answer:

1. x = ±9

2. $x=\pm \sqrt{13}$

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. $x^{2}-81=0$ i.e. $x^{2}=81$ i.e. x = ±9.

Problem 2. $2x^{2}-26=0$ i.e. $x^{2}-13=0$ i.e. $x^{2}=13$ i.e. $x=\pm \sqrt{13}$

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.