Question

Determine the value of a and b so that x^4 6x^3 +7x^2+ax+b is a perfect square

Answer 1

Explanation:

(Ax² + Bx + C)²

= (Ax² + Bx + C)(Ax² + Bx + C)

= Ax⁴ + 2ABx³ + 2ACx² + 2BCx + C².

By Comparing Coefficients, we have:

A = 1

2AB = 6

2AC = 7

2BC = a

C² = b

Solving them we get A = 1, B = 3 and C = 3.5.

Therefore a = 2BC = 2(3)(3.5) = 21,

b = C² = (3.5)² = 12.25.