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ijohnh14
03.07.2019 •
Mathematics
The expression f(x)=x³+ax²+bx+c leaves the same remainder,r, when it is divided by x+2 and when it is divided by x-2. evalute b. i need this as soon as possible (today )
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Ответ:
b = -4
Step-by-step explanation:
f(2) = R and f(-2) = R
Therefore f(2) = f(-2):-
(2)^3 + a(2)^2 + 2b + c = (-2)^3 +a(-2)^2 - 2b + c
8 + 4a + 2b+ c = -8 + 4a - 2b + c
The 4a and c cancel out. Then:-
8 + 2b = -8 - 2b
4b = -16
b = -4 answer
Ответ:
Consider this example: say we want to convert x = 11 0101 1001₂ to base 3.
The binary expansion of x is
x = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰
which in base 10 reduces to
x = 512 + 256 + 64 + 16 + 8 + 1 = 857
Recall the first several powers of 3:
3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729
Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.
• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or
857 = 1×729 + 128 = 1×3⁶ + 128
• How many times does 81 go into 128? Also 1 time, so
128 = 1×81 + 47 = 1×3⁴ + 47
• How many times does 27 go into 47? Also 1 time,
47 = 1×27 + 20 = 1×3³ + 20
• How many times does 9 go into 20? 2 times,
20 = 18 + 2 = 2×9 + 2 = 2×3² + 2
• How many times does 1 go into 2? Also 2 times,
2 = 2 + 1 = 2×1 + 0 = 2×3⁰
So we found
857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰
which is the ternary expansion of x,
x = 1 011 202₃