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AleksandrR [38]
3 years ago
6

Form a polynomial f(x) with real coefficients having the given degree and zeros.

Mathematics
1 answer:
dimaraw [331]3 years ago
6 0
There are many polynomials that fit the bill,
f(x)=a(x-r1)(x-r2)(x-r3)(x-r4)  where a is any real number not equal to zero.
A simple one is when a=1.
where r1,r2,r3,r4 are the roots of the 4th degree polynomial.
Also note that for a polynomial with *real* coefficients, complex roots *always* come in conjugages, i.e. in the form a±bi  [±=+/-]

So a polynomial would be:
f(x)=(x-(-4-5i))(x-(-4+5i))(x--2)(x--2)
or, simplifying
f(x)=(x+4+5i)(x+4-5i)(x+2)^2
=x^4+12x^3+77x^2+196x+164   [if you decide to expand]
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Step 1: Simplify both sides of the equation.

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Step 2: Subtract 6x from both sides.

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For this equation: a=65, b=384, c=585

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Step 3: Use quadratic formula with a=65, b=384, c=585

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  • x=−(384)±√(384)2−4(65)(585)/
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