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Calculus meets Functions

Review question

When does $3x^4 - 16x^3 +18x^2 + k = 0$ have four real solutions?
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Ref: R8959

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Suggestion

The equation in \(x\), \[3x^4 - 16x^3 +18x^2 + k = 0\] has four real solutions

when \(-27 < k < 5\);
when \(5< k <27\);
when \(-27< k <-5\);
when \(-5< k <0\).

Download GeoGebra file

The curve is the function \(y = 3x^4 - 16x^3 +18x^2 + k\).