Question

construct a polynomial function with least degree possible with real roots:-1/2,0,1/2 and (-2,f(-2))=(-2,6)

Answer 1

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Answer:

  f(x) = -0.8x^3 +0.2x

Step-by-step explanation:

For root 'a', one of the factors will be (x-a). For the three given roots, the factored form of the polynomial can be written ...

  f(x) = c(x -(-1/2))(x-0)(x -1/2) = cx(x^2 -1/4)

Then for x=-2, the value is ...

  f(-2) = c(-2)((-2)^2 -1/4) = -7.5c

  f(-2) = 6 = -7.5c

  c = -6/7.5 = -0.8

Then the polynomial can be written as ...

  f(x) = -0.8x^3 +0.2x