monic polynomial #!!
Algebra
Level
4
P(x) is a fourth degree monic polynomial, such that P(1)=10 , P(2)=20 , P(3)=30 . Evaluate (P(-8) + P(12)) / 10
The answer is 1984.
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1 solution
With 5 x 5 determinants, it is found that (0, 24) and (4, 40), an example in a pair at least, ought to be there with (1, 10), (2, 20) and (3, 30) specified for a monic polynomial of degree 4. For these, 24, 40 and 256 are plugged in to complete the tasks. As a consequence, f(-1) = 110 and f(5) = 74 etc. With all coefficients found by evaluating 6 determinants of 5 x 5:
f(x) = x^4 - 10 x^3 + 35 x^2 - 40 x + 24
f(-8) = 11800
f(12) = 8040
(11800 + 8040)/ 10 = 1984