Question

Which trinomial is a perfect square trinomial?
(Points : 1)
y^2 + 25y + 200

y^2 + 9y + 81

y^2 + 14y + 49

y^2 + 6y + 36

Answer 1

cancel out the first one and the second and the last. So, y^2 + 14y + 49 is a perfect square trinomial, if I remember correctly

Answer 2

A perfect square trinomial will have the following form:

\[(x+a)(x+a) = x^2 + 2ax + a^2\]

In other words, the coefficient of the \(x\) term, divided by 2 and squared, will give you the constant term.

For example, the first one is not a perfect square, because \((\frac{25}{2})^2 \ne 200\)

You can also use the discriminant of a quadratic in the form \(ax^2 + bx + c = 0\) to assess whether you have a perfect square. If \(\Delta = b^2-4ac = 0\), you have a perfect square trinomial.

Again, using the first one: \(a = 1, b = 25, c = 200\)
\[\Delta = b^2-4ac = (25)^2 - 4(1)(200) \ne 0\]so it is not a perfect square.