For the geometric sequence x, (2x + 1), (4x + 10), ... the value of x, to the nearest
1 answer:
Answer:
x ≈ 0.17
Step-by-step explanation:
There is a common ratio r between consecutive terms in a geometric sequence, that is
r = =
, substitute values
=
( cross- multiply )
x(4x + 10) = (2x + 1)² ← expand using FOIL
4x² + 10x = 4x² + 4x + 1 ( subtract 4x² + 4x from both sides )
6x = 1 ( divide both sides by 6 )
x = ≈ 0.17 ( to the nearest hundredth )
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Step-by-step explanation:
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<u><em>(FROM CROSS)</em></u>
Answer:
Error of Andrew: Made incorrect factors from the roots
Step-by-step explanation:
Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x). According to this definition:
(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.
Simplifying the brackets, we get:
(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.
This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.
So, the polynomial would be: