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maria [59]
2 years ago
13

Find a third degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.

Mathematics
1 answer:
Tanzania [10]2 years ago
6 0

Answer:

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is p(x) = x^{3}-5\cdot x^{2}-6\cdot x.

Step-by-step explanation:

From Fundamental Theorem of Algebra, we remember that the degree of the polynomials determine the number of roots within. Since we know three roots, then the factorized form of the polynomial function with the lowest degree is:

p(x) = (x-r_{1})\cdot (x-r_{2})\cdot (x-r_{3}) = 0 (1)

Where r_{1}, r_{2} and r_{3} are the roots of the polynomial.

If we know that r_{1} = -1, r_{2} = 0 and r_{3} = 6, then the polynomial function in factorized form is:

p(x) = (x+1)\cdot x \cdot (x-6) (2)

And by Algebra we get the standard form of the function:

p(x) = x\cdot (x+1)\cdot (x-6)

p(x) = x\cdot (x^{2}-5\cdot x -6)

p(x) = x^{3}-5\cdot x^{2}-6\cdot x (3)

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is p(x) = x^{3}-5\cdot x^{2}-6\cdot x.

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