Answer:
-10,10
Step-by-step explanation:
The given quadratic equation is
[tex]k {x}^{2} + 20x + k = 0[/tex]
The discriminant of this equation is given by;
[tex]D = {b}^{2} - 4ac[/tex]
where a=k, b=20, c=k
For rational solutions, the discriminant must be zero.
[tex] {20}^{2} - 4 \times k \times k = 0[/tex]
Simplify to get:
[tex]400 - 4 {k}^{2} = 0[/tex]
This implies that:
[tex]400 = 4 {k}^{2} [/tex]
[tex]100 = {k}^{2} [/tex]
Take square root to get:
[tex]k = \pm\sqrt{100} [/tex]
[tex]k = \pm10[/tex]
[tex]k = - 10 \: or \: k = 10[/tex]
