Step-by-step explanation:
[tex] \beta [/tex]
is a root of the quadratic
[tex]4 {x}^{2} - 10x + 5[/tex]
This quadratic isn't factorable so use the quadratic formula
[tex] - b + - \sqrt{ \frac{b {}^{2} - 4ac }{2a} } [/tex]
The plus and minus sign after b means we going to have two roots.
The roots are
[tex] \frac{5 + \sqrt{5} }{4} [/tex]
and
[tex] \frac{5 - \sqrt{5} }{4} [/tex]
We subsitue those values for Beta.
27a.
[tex] \frac{5}{2} [/tex]
27b.
25
