Question

If 16x2 + nx + 49 is the square of a

binomial, then what value could n be?
A.14
B.28
C.42
D.56

Answer 1

Th correct option is (d).

Explanation:

The given expression is :

`16x^2 + nx + 49` ....(1)

We know that, 16 = 4² and 49 = 7²

Also, (a+b)² = a²+2ab+b²

The given expression becomes,

`16x^2 + nx + 49=(4x)^2+nx+7^2\\\\=(4x)^2+2(4x)(7)+7^2\\\\=16x^2+56x+49\ ......(2)`

Comparing equations (1) and (2),

n = 56

Hence, the value of n is equal to 56.