Question

If a is a constant such that 4x^2 - 12x + a is the square of a binomial, then what is a?

Answer 1

Answer:

9

Step-by-step explanation:

Let that binomial be dx + c.

Square of dx + c is d²x² + c² + 2cdx

It means :

= > 4x² - 12x + a = d²x² + c² + 2dcx

Comparing values:

4x² = d²x² = > 4 = d² = > 2 = d

- 12x = 2dcx = > - 6 = dc = > - 6 = 2c = > - 3 = c

Remaining term = a = c²

So, from above c = - 3

= > c² = a = ( - 3 )² = 9

Hence the required value of a is 9.