Question

For what real values of $c$ is $4x^2 + 14x + c$ the square of a binomial?

Answer 1

Only for c = 49 the given expression is the square of a binomial.

For which values of c is the given expression the square of a binomial?

We want to find the values of c such that:

$4x^2 + 14x + c$

Is the square of a binomial.

Remember that:

$(a + b)^2 = a^2 + 2ab + b^2$

Now we can rewrite our expression as:

$(2x)^2 + 2*7*x + c$

If you compare that with the general binomial expansion, we can see:

$a = 2x$

$b = 7$

Then c must be equal to 7 squared:

$7^2 = 49 = c$

Only for c = 49 the given expression is the square of a binomial.

If you want to learn more about binomials:

https://brainly.com/question/13602562

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