Answer:
Solution of the quadratic equation [tex]x^{2}-16=0[/tex] is 4 and -4.
Step-by-step explanation:
The given quadratic equation is [tex]x^{2}-16=0[/tex]
To find the solutions of the quadratic equation, we first need to make the factors of [tex]x^{2}-16[/tex].
We know that we can write [tex]a^{2} -b^{2} =(a-b)(a+b)[/tex]
So, [tex]x^{2} -16[/tex] can be written as [tex]x^{2} -4^{2}[/tex], and it can be further written as [tex](x-4)(x+4)[/tex].
Now, on solving [tex]x^{2}-16=0[/tex] we have,
[tex]x^{2}-16=0[/tex]
[tex]x^{2} -4^{2}=0[/tex]
[tex](x-4)(x+4)=0[/tex]
So, either [tex]x-4=0[/tex] or [tex]x+4=0[/tex]
[tex]x=4[/tex] or [tex]x=-4[/tex]
Hence, the solution of the quadratic equation [tex]x^{2}-16=0[/tex] is 4 and -4.
