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jok3333 [9.3K]
3 years ago
6

Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 8−i, and passing through the orig

in.
Mathematics
1 answer:
9966 [12]3 years ago
5 0
Passing through the origin means that 0 is a root
for a polynomial with real coefients (an integer is real), if a+bi is a root, a-bi is also a root

so zeroes are
i,-i 8-i, 8+i and 0

the factors of an equation with factors r1,r2,r3 is
(x-r1)(x-r2)(x-r3)

so
zeroes of i,-i,8-i, 8+i, 0 is
(x-i)(x+i)(x-(8-i))(x-(8+i))(x-0)
expanded
x^5-16x^4+66x^3-16x^2+65x

the polynomial is x^5-16x^4+66x^3-16x^2+65x
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ipn [44]

[ a⁵ (a²b³)⁵ ] / [ a²b⁻² ]

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I think this: a⁴⁸b⁷⁷ is the answer.

Hope this helps :)


5 0
4 years ago
How many sides does a regular polygon have if its interior angles are 150
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