?For what values of $c$ is there a straight line that intersects the curve\(y=x^{4}+c

Chapter 15, Problem 22

(choose chapter or problem)

For what values of $c$ is there a straight line that intersects the curve

$y=x^{4}+c x^{3}+12 x^{2}-5 x+2$

in four distinct points?

Equation Transcription:

$c$

$y={x}^{4}+c{x}^{3}+12{x}^{2}-5x+2$

Text Transcription:

y=x^4+cx^3+12x^2-5x+2

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?For what values of \(c\) is there a straight line that intersects the curve\(y=x^{4}+c