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