Question

Find a polynomial with the given zeros calculator.

A) Use the rational root theorem
B) Apply the Remainder theorem
C) Factor by grouping
D) Find the sum and product of roots

Answer 1

To find a polynomial from its zeros, you can use the rational root theorem, apply the Remainder theorem, factor by grouping, or if it's a quadratic equation, use the sum and product of roots to reconstruct the polynomial.

Step-by-step explanation:

The subject in question is Mathematics, more specifically, it's about finding a polynomial using its given zeros. In order to find a polynomial from its given zeros, you can use several methods:

1. Use the rational root theorem to identify all possible rational zeros of the polynomial.
2. Apply the Remainder theorem to test each possible zero by evaluating the polynomial at that number and checking if the remainder is zero.
3. Factor by grouping if the polynomial has four terms and can be grouped in such a way to factor by common terms.
4. Find the sum and product of roots if it's a quadratic equation (ax²+bx+c=0), where knowing the sum and product of roots can help reconstruct the original polynomial.

For quadratic equations, the roots can be found using the formula x = (-b ± √(b²-4ac))/(2a). When using a calculator such as the TI-83, 83+, or 84, you can use built-in functions to solve for the roots.

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