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A certain cubic polynomial y=f(x) cuts the x-axis at the three points x=10, 100 and 1000. Is this enough information to determine the location of its point of inflection (note that this is not necessarily a stationary point of inflection)? If so, where is this point; if not, why not?
Construct a cubic polynomial which cuts the x-axis at x=10, 100 and its point of inflection. How many such polynomials are there?
Cubic Roots
Age 16 to 18
ShortChallenge Level 
A certain cubic polynomial y=f(x) cuts the x-axis at the three points x=10, 100 and 1000. Is this enough information to determine the location of its point of inflection (note that this is not necessarily a stationary point of inflection)? If so, where is this point; if not, why not?
Construct a cubic polynomial which cuts the x-axis at x=10, 100 and its point of inflection. How many such polynomials are there?
Did you know ... ?
Polynomials have many fascinating properties. A key result of university mathematics is the Fundamental Theorem of Algebra which states that any polynomial of degree n p(z)= a_nz^n+a_{n-1}z^{n-1}+\dots+a_0, with a_n\neq 0, has precisely n, possibly repeated, complex number solutions.
Polynomials have many fascinating properties. A key result of university mathematics is the Fundamental Theorem of Algebra which states that any polynomial of degree n p(z)= a_nz^n+a_{n-1}z^{n-1}+\dots+a_0, with a_n\neq 0, has precisely n, possibly repeated, complex number solutions.
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