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Lubov Fominskaja [6]

3 years ago

14

Calculate the gcd(f(x),g(x)) for the indicated f(x) and g(x) in the polynomial ring F[x]. Also find u(x) & v(x) such that gc

d(f(x),g(x))=u(x)f(x)+v(x)g(x).
f(x)=x^4 - x^2 - 2
g(x)=x^3 + x^2 + x + 1
in Q[x]

1 answer:

Artist 52 [7]3 years ago

8 0

Answer:

l

Step-by-step explanation:

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Answer:

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Part 2) The solutions are

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Step-by-step explanation:

we know that

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so

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The discriminant is equal to

$D=(b^{2}-4ac)$

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If D>0 -----> the quadratic equation has two real solutions

If D<0 -----> the quadratic equation has two complex solutions

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$D=8^{2}-4(1)(20)=-16$ -----> the quadratic equation has two complex solutions

<em>Find out the solutions</em>

substitute the values of a,b and c in the formula

$x=\frac{-8(+/-)\sqrt{8^{2}-4(1)(20)}} {2(1)}$

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Remember that

$i=\sqrt{-1}$

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$x_1=\frac{-8(+)4i} {2}=-4+2i$

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Step-by-step explanation:

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