Let $$P(x)$$ be a polynomial of least degree whose graph has three points of inflextion $$($$–$$1$$, –$$1)$$, (1$$,$$1) and a point with abscissa $$0$$ at which the curve is inclined to the axis of abscissas at an angle of $$60$$∘

Question

Let $$P(x)$$ be a polynomial of least degree whose graph has three points of inflextion $$($$–$$1$$, –$$1)$$, (1$$,$$1) and a point with abscissa $$0$$ at which the curve is inclined to the axis of abscissas at an angle of $$60$$∘

Infinity Learn · Accepted Answer

we have P′′$$(x)=a(x+1)x(x$$−$$1)=ax3$$−x⇒P′$$(x)=a14x4$$−$$12x2+b$$⇒$$P(x)=a120x5$$−$$16x3+bx+cAs$$−$$1=a$$−$$120+16$$−$$b+c1=a120$$−$$16+b+c$$⇒$$c=0and$$ $$1=$$−$$760a+bAlso$$ $$3=b$$⇒$$a=60(3$$−$$1)/7we$$ have ∫$$01$$ $$P(x)dx=$$−$$130a+12b=27(1$$−$$3)+32$$

Let $P (x)$ be a polynomial of least degree whose graph has three points of inflextion (–1, –1), (1,1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissas at an angle of $60^{\circ}$

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Let P(x) be a polynomial of least degree whose graph has three points of inflextion (–1, –1), (1,1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissas at an angle of 60∘

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Let $P (x)$ be a polynomial of least degree whose graph has three points of inflextion (–1, –1), (1,1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissas at an angle of $60^{\circ}$