## If X2 + Mx + M Is A Perfect-Square Trinomial, Which Equation Must Be True?

Question

1. When it comes to perfect-square trinomials, the equation “X2 Mx M” is a classic example. This type of equation is often used to illustrate basic algebra concepts, such as factoring and solving for unknowns. To determine which equation must be true in order for this trinomial to be considered a perfect-square, it’s important to understand how perfect-squares are formed.

At its core, a perfect-square trinomial consists of three terms that result in the square of a binomial when simplified. In other words, if X2 Mx M is a perfect square trinomial, then (X + M)2 must equal X2 + 2MX +M2. This means that the following equation must be true: 2M = 0.

2. Did you know that if X2 + Mx + M is a perfect-square trinomial, then there must be an equation that is true?

It’s true! A perfect-square trinomial is a polynomial in which all the terms are perfect squares. For example, x2 + 6x + 4, is a perfect-square trinomial because all of the terms are perfect squares (x2, 6x, and 4).

So, if X2 + Mx + M is a perfect-square trinomial, then the equation that must be true is M2 = 4M. This equation is true because it states that the constant in the trinomial (M) must be a perfect square, which is necessary for a perfect-square trinomial.

To make things simpler, let’s look at an example. Say, X2 + 8x + 16 is a perfect-square trinomial. Then, the equation that must be true is 82 = 4(8). And yes, this is true, which means the trinomial is actually a perfect-square trinomial.

Now that you know what the equation is, you should also know that it can be used to solve for M. All you have to do is take the square root of both sides of the equation to get M = ±4. Then, you can use this value of M to solve for X in the trinomial.

So, there you have it! If X2 + Mx + M is a perfect-square trinomial, then the equation that must be true is M2 = 4M. With this equation, you can solve for M and X to find the values of the trinomial.