Question

Find the values of a and b if 16x4 - 24' +(a-1)x' +(6+1)x+49 is a perfect​

Answer 1

Answer:

Since the leading term is 16x^4 and the constant term is 49, the perfect square must be of the form %284x%5E2%2Bnx%2B7%29%5E2 or 4x%5E2%2Bnx-7%29%5E2.

Each form gives an answer to the question.

(1) For the first form...

%284x%5E2%2Bnx%2B7%29%5E2+=+16x%5E4%2B8nx%5E3%2B%28n%5E2%2B56%29x%5E2%2B14nx%2B49

Then

8n = -24 --> n = -3

n^2+56 = 65 = a-1 --> a = 66

14n = -42 = b+1 --> b = -43

(2) For the second form...%284x%5E2%2Bnx-7%29%5E2+=+16x%5E4%2B8nx%5E3%2B%28n%5E2-56%29x%5E2-14nx%2B49

Then

8n = -24 --> n = -3

n^2-56 = -47 = a-1 --> a = -46

-14n = 42 = b+1 --> b = 41

Answer: Two solutions

(1) a=66, b=-43

Hope it is good mate!!