For what value of the parameter $k$ $k$ does the curve function $y = x^{3} + k x + k^{2} - 6 k + 5$ $y=x^3+kx+k^2−6k+5$ passes through the origin?

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Answer 1 · 2017-04-09T06:09:32

$k = 1$ $k=1$ and $k = 5$ $k = 5$

Given: $y = x^{3} + k x + k^{2} - 6 k + 5$ $y=x^3+kx+k^2−6k+5$

Substitute 0 for both x and y:

$0 = 0^{3} + k (0) + k^{2} - 6 k + 5$ $0=0^3+k(0)+k^2−6k+5$

$0 = k^{2} - 6 k + 5$ $0 = k^2−6k+5$

Factor

$(k - 1) (k - 5) = 0$ $(k-1)(k-5)= 0$

$k = 1$ $k=1$ and $k = 5$ $k = 5$

For what value of the parameter kk does the curve function y=x3+kx+k2−6k+5y=x^3+kx+k^2−6k+5 passes through the origin?