Find the missing length indicated
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An expression has numbers, variables, and mathematical operations. The equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
<h3>What is an Expression?</h3>In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
A perfect square trinomial is in the form (a+b)²=a²+b²+2ab. If we compare the perfect square trinomial x²+mx+m, we will get that the value of m should be such that it satisfies the equation . Since there is only one value that can satisfy this equation that is 2.
Therefore, the equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
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Answer:
Step-by-step explanation:
We have the quadratic equation i.e.
As, the roots of the quadratic equation are given by
.
So, from the given equation, we have,
a = 1, b = -36 , c = -324.
Substituting the values in , we get,
i.e.
i.e.
i.e.
i.e. and
i.e. and
i.e. x = 43.45 and x = -7.45
Thus, the roots of the equation are 43.45 and -7.45.
Hence, the factored form of the given expression will be