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2 answers:
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Answer: (5 - √1) and (4 + √7)
Step-by-step explanation:
Here we have 4 roots, then this is a polynomial of 4th degree.
We can write it as
a*x⁴ + b*x³ + c*x² + d*x + e = 0
We could rewrite this as the product of two quadratic equations:
(a₁*x² + b₁*x + c₁)*(a₂*x² + b₂*x + c₂) = 0
This will be equal to zero when (a₁*x² + b₁*x + c₁) is equal to zero, and when
(a₂*x² + b₂*x + c₂) is equal to zero.
Then we need to find the roots of these two quadratic equations.
And we know that the roots of a quadratic equation like:
a₁*x² + b₁*x + c₁ are given by:
Then the general form of the roots is something like:
This means that if one of the roots is:
5 + √1, we must have another root equal to 5 - √1
And if we have one root equal to 4 - √7, then we must have another root equal to 4 + √7
Then the correct options are:
(5 - √1) and (4 + √7)
Answer:
(i) The length of AC is 32 units, (ii) The length of BC is 51 units.
Step-by-step explanation:
(i) Let suppose that AB and BC are collinear to each other, that is, that both segments are contained in the same line. Algebraically, it can be translated into this identity:
If we know that and
, then:
The length of AC is 32 units.
(ii) Let suppose that AB and AC are collinear to each other, that is, that both segments are contained in the same line. Algebraically, it can be translated into this identity:
If we know that and
, then:
The length of BC is 51 units.