Question

What value of b makes the trinomial below a perfect square x^2-bx+36?

Answer 1

(Half of b)²=36
half of b=6 or half of b=-6
b=12 or b=-12

Note: the perfect square is either (x+6)² or (x-6)²

Answer 2

-12 and 12.

Explanation:

The given trinomial is

`x^2-bx+36`

A trinomial
`Ax^2+Bx+C` is a perfect square trinomial if

`B^2-4AC=0` ....(1)

In the given trinomial A=1, B=-b and C=36. Substitute these values in equation (1).

`(-b)^2-4(1)(36)=0`

`b^2-144=0`

`b^2=144`

Taking square root on both sides.

`b=\pm √(144)`

`b=\pm 12`

Therefore, the possible values of b are -12 and 12.