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Question Number 107779 by ajfour last updated on 12/Aug/20

Commented by ajfour last updated on 12/Aug/20

$$y=(x-p)(x^3-39x-70)$$$$Findp.$$

Commented by Sarah85 last updated on 12/Aug/20

$$\mathrm{impossible}\mathrm{under}\mathrm{given}\mathrm{conditions}$$$$\mathrm{tangent}\mathrm{through}(-2\mid 0)\mathrm{and}(\frac{3p}{5}\mid y)\mathrm{leads}\mathrm{to}$$$$p=-\frac{10}{3}\Rightarrow \frac{3p}{5}=-2\mathrm{and}\mathrm{the}\mathrm{tangent}\mathrm{is}\mathrm{at}$$$$(-2\mid 0)$$

Commented by ajfour last updated on 13/Aug/20

$$thanksanyway..$$

Answered by floor(10²Eta[1]) last updated on 13/Aug/20

$$\frac{3\mathrm{p}}{5}>7\Rightarrow \mathrm{p}>\frac{35}{3}\approx 11,6$$$$\mathrm{y}=(\mathrm{x}-\mathrm{p})({\mathrm{x}}^3-39\mathrm{x}-70)$$$$\mathrm{y}={\mathrm{x}}^4-{39\mathrm{x}}^2-70\mathrm{x}-{\mathrm{px}}^3+39\mathrm{px}+70\mathrm{p}$$$${\mathrm{y}}^{\prime }={4\mathrm{x}}^3-{3\mathrm{px}}^2-78\mathrm{x}-70+39\mathrm{p}$$$$\mathrm{x}=-2\Rightarrow {\mathrm{y}}^{\prime }=0\Rightarrow \mathrm{p}=-2$$$$\mathrm{but}\mathrm{p}>11$$$$$$

Commented by Sarah85 last updated on 13/Aug/20

$${\mathrm{that}}^{\prime }\mathrm{s}\mathrm{what}\mathrm{I}\mathrm{wrote}\mathrm{before}$$

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