Question

What number goes in the box so that \[x^2 + \boxed{\phantom{00}}x + 100\]is the square of a binomial? If you find more than one, give your answer as a list.

Answer 1

Since $100=(\pm10)^2$, the idea here is to find $b$ such that

$(x\pm10)^2=x^2+bx+100$

Expanding the left side completely, we find two possibilities:

$x^2\pm20x+100$

so that $b$ can be either positive or negative 20.

Answer 2

The answer will be ±20

Let us consider a binomial (x ± a)

now squaring it we get      $x^{2}$ ± 2ax + $a^{2}$

If we compare it to the question we get  $a^{2} =$ 100

                                                                 ⇒ a = ±10

According to the question we have to find the value of  2a

                            2a = 2×(±10) = ±20

Hence ±20 is the answer.

Learn more about binomial expansion:

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