Mathematics, 25.01.2022 03:40, Hunter1471
Find a polynomial P(x) with a degree of three and zeros -2,3,5 and passing through the point (2,24)
Answers: 3
![\begin{cases} x=-2\implies &x+2=0\\ x=3\implies &x-3=0\\ x=5\implies &x-5=0 \end{cases}~\hfill a(x+2)(x-3)(x-5)=\stackrel{0}{y} \\\\\\ \stackrel{\textit{we also know that}}{x = 2\qquad y = 24}\qquad \implies a(2+2)(2-3)(2-5)=24 \\\\\\ a(4)(-1)(-3)=24\implies 12a=24\implies a=\cfrac{24}{12}\implies \underline{a=2} \\\\[-0.35em] ~\dotfill](/tpl/images/2631/5807/bc6bc.png)
![2(x+2)(x-3)(x-5)=y\implies 2(x+2)\stackrel{F~O~I~L}{(x^2-8x+15)}=y \\\\\\ 2(x^3-8x^2+15x+2x^2-16x+30)=y\implies 2(x^3-6x^2-x+30)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2x^3-12x^2-2x+60=y~\hfill](/tpl/images/2631/5807/a7575.png)
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Find a polynomial P(x) with a degree of three and zeros -2,3,5 and passing through the point (2,24)...
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