Question

Find all Values of b that will make the polynomial a perfect square trinomial.

25z^2+bz+36
Please write out how to do this so I can see the steps of what I am doing wrong. thank you!

Answer 1

There are two solutions for
`b`:
`b = + 30\cdot z`,
`b = -30\cdot z`

Explanation:

By Algebra, we know that a polynomial is a perfect square trinomial if it is of the form:

`a^(2) + 2\cdot a \cdot c + c^(2) = (a + c)^(2)` (1)

By direct comparison, we have the following system:

`a^(2) = 25\cdot z^(2)`,
`c^(2) = 36`,
`2\cdot a \cdot c = b`.

There are two possible solutions for
`b`:

1)
`a = \pm 5\cdot z`,
`c = \pm 6`,
`b = + 30\cdot z`

2)
`a = \pm 5\cdot z`,
`c = \mp 6`,
`b = -30\cdot z`