Given:
The quadratic equation is:
[tex]x^2+13x+k=0[/tex]
[tex]x_1=-9[/tex]
To find:
The value of k and [tex]x_1[/tex].
Solution:
We have,
[tex]x^2+13x+k=0[/tex] ...(i)
Putting [tex]x=-9[/tex], we get
[tex](-9)^2+13(-9)+k=0[/tex]
[tex]81-117+k=0[/tex]
[tex]-36+k=0[/tex]
[tex]k=36[/tex]
Putting [tex]k=36[/tex] in (i), we get
[tex]x^2+13x+36=0[/tex]
Splitting the middle term, we get
[tex]x^2+9x+4x+36=0[/tex]
[tex]x(x+9)+4(x+9)=0[/tex]
[tex](x+9)(x+4)=0[/tex]
[tex]x=-9,-4[/tex]
Here, [tex]x_1=-9[/tex] and [tex]x_2=-4[/tex].
Therefore, the required values are [tex]k=36[/tex] and [tex]x_2=-4[/tex].
