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Construct a polynomial function of least degree possible using the given information.

Real roots: −1, 1, 3 and (2,f(2))=(2,5) 

 Oct 14, 2018

Best Answer 

 #1
avatar+3628 
+1

\(\text{the polynomial will be of the form}\\ p(x) = k(x+1)(x-1)(x-3) \\ p(2) = k(3)(1)(-1) = 5 \\ -3k = 5 \\ k=-\dfrac 5 3 \\ p(x) = \dfrac 5 3 (x+1)(x-1)(x-3) \\ p(x) = -\dfrac{5 x^3}{3}+5 x^2+\dfrac{5 x}{3}-5\)

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 Oct 14, 2018
 #1
avatar+3628 
+1
Best Answer

\(\text{the polynomial will be of the form}\\ p(x) = k(x+1)(x-1)(x-3) \\ p(2) = k(3)(1)(-1) = 5 \\ -3k = 5 \\ k=-\dfrac 5 3 \\ p(x) = \dfrac 5 3 (x+1)(x-1)(x-3) \\ p(x) = -\dfrac{5 x^3}{3}+5 x^2+\dfrac{5 x}{3}-5\)

Rom Oct 14, 2018

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