Question

What are the values of `a` and `b` if `4x^4 - 12 x^3+37x^2 + ax + b` is a perfect square?

Answer 1

See below.

Explanation:

Making

`(2x^2+c_1 x+ c_2)^2 = 4x^4 - 12 x^3+37x^2 + ax + b`

and grouping coefficients we have

`{(b = c_2^2), (a = 2 c_1 c_2), (37 = c_1^2 + 4 c_2), (-12 =4 c_1):}`

and solving we get

`c_1 -3, c_2 = 7, a = -42, b = 49` or

`(2x^2-3 x+ 7)^2 = 4x^4 - 12 x^3+37x^2 -42x +49`