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kiruha [24]
2 years ago
15

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

Mathematics
1 answer:
kondor19780726 [428]2 years ago
8 0

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.

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