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The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts of the graph of $f$?

Guest Apr 29, 2017
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 #1
avatar+6711 
+1

The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts of the graph of $f$?

 

\(f(x)=y=ax^3+bx^2+cx+d\)

 

\(P_1(-1/15)\\P_2(0/0)\\P_3(1/-5)\\P_4(2/12)\)

 

\(y=ax^3+bx^2+cx+d\)

 

\(15=-a+b-c+d\)                     

\(0=d\)

\(-5=a+b+c +d\)

\(12=8a+4b+2c+d\)

 

a, b, c, d from the four linear equations comes slightly later.

 

laugh  !

asinus  Apr 29, 2017
edited by asinus  Apr 29, 2017
 #2
avatar+25997 
+1

a = 2, b = 5, c = -12, d = 0

Alan  Apr 29, 2017

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