Question

Find the value of k and x2 x^2+ 13x + k = 0, x1=-9

Answer 1

Given:

The quadratic equation is:

$x^2+13x+k=0$

$x_1=-9$

To find:

The value of k and $x_1$.

Solution:

We have,

$x^2+13x+k=0$                ...(i)

Putting $x=-9$, we get

$(-9)^2+13(-9)+k=0$

$81-117+k=0$

$-36+k=0$

$k=36$

Putting $k=36$ in (i), we get

$x^2+13x+36=0$

Splitting the middle term, we get

$x^2+9x+4x+36=0$

$x(x+9)+4(x+9)=0$

$(x+9)(x+4)=0$

$x=-9,-4$

Here, $x_1=-9$ and $x_2=-4$.

Therefore, the required values are $k=36$ and $x_2=-4$.