If x2 mx m is a perfect-square trinomial, which equation must be true?.

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09-03-2022
Mathematics

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If x2 mx m is a perfect-square trinomial, which equation must be true?.

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ap8997154 ap8997154 · Answer 1 · 2022-03-17T11:12:12+01:00

Expression consist of numbers, variables, and mathematical operations. The equation that is true is x²+mx+m= (x+2)².

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

As it is given that the x²+mx+m is a perfect square trinomial, and we know that the general equation of perfect square trinomial is given as,

ax²+bx+c=0

where a,b and c are real numbers, and a≠0,

if we compare the equation with our equation

[tex]ax^2+bx+c=0\\x^2+mx+m=0[/tex]

We will get the value of 'a' as 1, b=c=m, therefore, we need a binomial which is when expanded then in its perfect square trinomial the value of b=c, therefore, the only feasible option here is (x+2)².

Hence, the equation that is true is x²+mx+m= (x+2)².

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