Let p(x) be a fourth degree polynomial with a leading coefficent 2 such that p(-2) = 34, p(-1) = 10, p(1) = 10, and p(2) = 34. Find p(0)???
2 Answers
Explanation:
we want
so we only need to find the value for
To do that we will use the information given.
giving
similarly
adding
giving
p(-1)=2-b+c-d+e=10#
giving
Adding
so we have
subtract
Explanation:
From the values given, we can tell that
#p(x) = 2x^4+ax^2+b#
Then using the given values, we have:
#10 = p(1) = 2+a+b" "# and hence#" "a+b=8#
#34 = p(2) = 32+4a+b" "# and hence#" "4a+b=2#
Subtracting the first of these equations from the second, we get:
#3a=-6" "# and hence#" "a=-2#
Then from the first equation:
#b = 8-a = 8-(-2) = 10#
So:
#p(0) = 0+0+b = 10#