SOLUTION: Find a polynomial function of degree 3 with coefficients that satisfies the given conditions of having zeros of -5, -5 and 0.
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Question 324129: Find a polynomial function of degree 3 with coefficients that satisfies the given conditions of having zeros of -5, -5 and 0.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find a polynomial function of degree 3 with coefficients that satisfies the given conditions of having zeros of -5, -5 and 0.
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f(x) = x(x+5)(x-5) = x(x^2-25) = x^3-25x
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is a zero of a polynomial if and only if 
is a factor of of the polynomial.
Every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity.
Therefore the complete set of factors for the desired polynomial is:
\right)\left(x\ -\ (-5)\right)\left(x\ -\ (0)\right))
All you need to do to specify one of the infinite set of polynomials that fits the requirement is to multiply:
\left(x\ +\ 5\right)\left(x\right))
Just multiply it out.
John
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