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