Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D. They form line segments
2 answers:
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Answer:
imaginary roots
Step-by-step explanation:
For a quadratic in the form ...
the discriminant is ...
You have a=1, b=-6, c=12, so the discriminant is ...
d = (-6)² -4(1)(12) = 36 -48 = -12
When the discriminant is negative, both roots are complex. When the discriminant is not a perfect square, both roots are irrational. Here, the discriminant is negative and not a perfect square, so the roots are complex with an irrational imaginary part.
The best single descriptor is <em>imaginary root</em>.
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The roots are (-b±√d)/(2a) = (6 ± 2i√3)/2 = 3 ± i√3. These roots have a rational real part and an irrational imaginary part. When the number with an imaginary part has a non-zero real part, it is called "complex", rather than "imaginary."
Answer:
f(x) = (x - 3)(x + 1) → Corresponds with the first (raised higher ) ∪ shaped graph
f(x) = -2(x - 1)((x + 3) → Corresponds with the ∩ shaped graph
f(x) = 0.5(x - 6)((x + 2) → Corresponds with the second (lower) ∪ shaped graph
Step-by-step explanation:
For the function f(x) = (x - 3)(x + 1)
We have;
When x = 0, y = -3
When y = 0 x = 3 or -1
Comparing with the graphs, it best suits the first ∪ shaped graph that rises here than the other ∪ shaped graph
For the function;
f(x) = -2(x - 1)((x + 3)
When x = 0, y = 6
When y = 0, x = 1 or -3
Which corresponds with the ∩ shaped graph
For the function;
f(x) = 2(x + 6)((x - 2)
When x = 0, y = -24
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = 0.5(x - 6)((x + 2)
When x = 0, y = -6
When y = 0, x = 6 or -2
Which best suits the second ∪ shaped graph that is lower than the other (first) ∪ shaped graph
For the function;
f(x) = 0.5(x + 6)((x - 2)
When x = 0, y = -6
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = (x + 3)((x - 1)
When x = 0, y = -3
When y = 0, x = -3 or 1
Graph not included
