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Question 839476: if f(-3)=-120, for f(x)=x^4+x^3-19x^2+kx+30.. find f(1)
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To find f(1), we need to first find k in our function. We do this by replacing each of our x's with -3 and setting that equal to -120:
(-3)^4 + (-3)^3 - 19(-3)^2 + k(-3) + 30 = -120 ----->
81 + (-27) - 19(9) - 3k + 30 = -120 ----->
81 - 27 - 171 - 3k + 30 = -120 ----->
-3k - 87 = -120
Next, we will add 87 to both sides of our equation, which will give us:
-3k = -33
Dividing both sides of our equation by -3 will give us the value of k:
k = 11
Now, we can replace k with 11 in our function and replace all of the x's with 1:
(1)^4 + (1)^3 - 19(1)^2 + (11)(1) + 30 ----->
1 + 1 - 19 + 11 + 30 ----->
24
Therefore, our answer is 24
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