What is the sum of all possible values of for which x^2 + kx - 10x + 36 is the square of a binomial?

Guest Jul 17, 2021

edited by
Guest
Jul 17, 2021

#1**0 **

*What is the sum of all possible values of for which x^2 + kx - 10x + 36 is the square of a binomial?*

For the square of the binomial to end with +36, the binomial must be either (x + 6)^{2} or (x – 6)^{2}.

So (kx – 10x) has to equal either +12x or –12x.

If (kx – 10x) equals +12x, then k is +22.

If (kx – 10x) equals –12x, then k is –2.

The sum of +22 and –2 is **20**.

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Guest Jul 18, 2021