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Ivanshal [37]
3 years ago
15

What is The polynomial for the question above

Mathematics
1 answer:
frosja888 [35]3 years ago
4 0
A polynomial of degree n with roots r_1,r_2,...,r_n can be represented as: f(x)=A(x-r_1)(x-r_2)\cdot...\cdot(x-r_n), where A is a constant (The same "a" that appears outside the parentheses in the field where you will type the polynomial). In this question, the number of roots is 4, because the degree of f(x) is 4. If a polynomial has only real coefficients, the complex roots appear in pairs of conjugates. So, since -3+4i is a zero, -3-4i is a zero too. Then, we have the 4 zeros. Hence, f(x) will be in the form:

f(x)=A(x-5)^2(x-(-3+4i))(x-(-3-4i))\\\\f(x)=A(x-5)^2(x^2-(-3+4i)x-(-3-4i)x+(-3+4i)(-3-4i))\\\\f(x)=A(x^2-10x+25)(x^2+6x+25)\\\\f(x)=A(x^4-4x^3-10x^2-100x+625)


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