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

Answer:

$k=\pm 6$

Step-by-step 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, $\alpha +\beta =\dfrac{-b}{a}$

$\alpha +\beta =\dfrac{-(-k)}{1}\\\\\alpha +\beta =k\\\\3\beta =k\ .......(1)$

Product of roots,

$\alpha \beta =\dfrac{c}{a}\\\\2\beta ^2=\dfrac{8}{1}\\\\\beta =\pm 2$

If $\beta =\pm2$,

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

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