Help Polynomials Question (1 Viewer)

kevinsta · Apr 13, 2014

Given two roots of 2x^3 -kx^2+8=0 are equal, find k.

Need help on this question so hard.

Kurosaki · Apr 13, 2014

kevinsta said:
Given two roots of 2x^3 -kx^2+8=0 are equal, find k.

Need help on this question so hard.

Let the roots be alpha, alpha and beta.
Using sum of roots, then $2\alpha +\beta=\frac{k}{2}$
Using product of roots, $\alpha^2\beta=-4$
Using sum of roots two at a time, then $\alpha^2+2\alpha\beta=0$
We can rearrange that last one to be: $2\alpha\beta=-\alpha^2$ , from which follows: $\alpha\beta=\frac{-\alpha^2}{2}$
We can substitute that into the product of roots, giving us $\frac{-\alpha^3}{2}=4$ .
From here, solve for alpha, then beta, and hence deduce k by sum of roots.

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Help Polynomials Question (1 Viewer)

kevinsta

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Kurosaki

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