9514 1404 393
Eexplanation:
16. Suppose the roots are α and kα. Then we can write the equation as ...
a(x -α)(x -kα) = 0
ax² -ax(α +kα) +akα² = 0
Comparing to the original equation, we can equate coefficients to get ...
Solving the first for α gives ...
α = -b/(a(1+k)
Substituting into the second, we have ...
c = ak(-b/(a(1+k)))²
Multiplying by a(1+k)², we get ...
(1+k)²ac = kb²
Using k=2 gives ...
9ac = 2b² . . . . . as required
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17. Using the previous result with k=1 (equal roots), we have ...
(1+k)²ac = kb²
4ac = b² . . . . . for k=1
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<em>Additional comment</em>
We observed that the problems were similar, but had different factors relating the roots. So, we elected to solve the general case, then fill in the specific values for the two problems.
Answer:
The first one
Step-by-step explanation:
Answer:
4 .For 32 it goes into 4 and for 12 it goes into 4
Step-by-step explanation:
Answer:
d)
Step-by-step explanation:
the polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r). In particular, x-r is a divisor (that means a factor) of f(x), if and only if f(r)=0.
our r here is -1 to get x + 1.
f(-1) = 2×(-1)³ + 5×(-1)² - -1 - 6 = -2 + 5 + 1 - 6 = -2
the remainder is -2.
and since the remainder is <> 0, the binomial cannot be a factor.
Answer:
Step-by-step explanation:
P of red or green = (40 red+ 10 green)/ (40 red +50 yellow+10 green)
= 50/ 100= 1/2
