Answer: d.
Explanation:-
- The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
- Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.
Thus only option d. with degree 6 has exactly 6 roots.
Answer:
- the value of the function changes sign in the interval
- the function is monotonic in the interval
Step-by-step explanation:
All polynomial functions are continuous, so we know from the intermediate value theorem that if the expression on the left changes sign in the interval [-2, 1] then there will be a zero in that interval. If the function is monotonic in the interval, there can only be one zero.
a) For f(x) = x^3 +x +3 = (x^2 +1)x +3, the values at the ends of the interval are ...
f(-2) = (4+1)(-2) +3 = -7
f(-1) = (1 +1)(-1) +3 = 1
The function value goes from -7 to +1 in the interval, so there exists at least one root in that interval.
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b) The derivative of the function is ...
f'(x) = 3x^2 +1
This is positive for any x, so is positive in the interval [-2, -1]. That is, the function is continuously increasing in that interval, so cannot have more than one crossing of the x-axis. There is exactly one root in the interval [-2, -1].
Answer: Yes; you do combine "-w" and "4w" ; because they are both "like terms" ; that is, they are both terms with the SAME first degree single variable in the entire expression.
So, to combine them:
-w + 4w = -1w + 4w = 3w ;
and we can simplify the entire expression:
" -w + 4w + 12 " ;
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to: " 3w + 12 " .
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Hope this explanation helps!
Answer: -12
Step-by-step explanation:
To get from -5 to 12, you'd add 7
So to get to the first, subtract 7 from -5
Pythagoras theorem ! (a²+b²=c²)
Q1) AC = √4.8²+3.6²
= √36
= 6cm
Q2) AB= √17.55² - 6.75²
= √262.44
= 16.2cm
Q3) BC= √14² - 6²
= √160
= 12.64911
= 12.6 cm (to 3sf)
