Question

Find the values of a and b such that x^2 + 3x + 4 = (x + a)^2+ b

Answer 1

Answer:

$x {}^{2} + 3x + 4 = (x + a) {}^{2} + b \\ x {}^{2} + 3x + 4 = x {}^{2} + 2ax + a {}^{2} + b \\ = x {}^{2} + a {}^{2} + 2ax + b \\ 2a = 3 \\ b = 4 \\ a = \frac{3}{2} \\ b = 4$