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The polynomial

f(x) = x^3 + 10x^2 + 27x - 38

has one integer root. What is it?

 May 26, 2021
 #1
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The integer root is 19.

 May 26, 2021
 #2
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Look at the coefficients of the powers of x.  These are 1, 10 and 27.  Their sum is  1+10+27 = 38.  Hence, if x = 1 then f(x) = 0, so the integer root is x = 1.

 May 26, 2021

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