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`.