Question

Find the possible values of k if one of the roots of the quadratic equation x^2 - kx + 8 = 0 is twice the other.​

Answer 1

`k=\pm 6`

Explanation:

The given quadratic equation is :

`x^2 - kx + 8 = 0`

One of the roots of this equation is twice that of the other. Let the roots are
`\alpha \ and\ \beta`,
`\alpha =2\beta`

Sum of roots,
`\alpha +\beta =(-b)/(a)`

`\alpha +\beta =(-(-k))/(1)\\\\\alpha +\beta =k\\\\3\beta =k\ .......(1)`

Product of roots,

`\alpha \beta =(c)/(a)\\\\2\beta ^2=(8)/(1)\\\\\beta =\pm 2`

If
`\beta =\pm2`,

`k=3(2)\\\\=\pm 6`

So, the value of k is equal to
`\pm 6`.