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For what real values of c is 4x^2 + 14x + c - 2x^2 - 10x the square of a binomial?

May 15, 2022

#1
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Simplify first.

$$4x^2 + 14x +c -2x^2 - 10x = 2x^2 + 4x + c$$.

If this is a square of a binomial, its discriminant is zero.

$$4^2 - 4(2)(c) = 0 \\ 8c = 16\\ c = 2$$

May 15, 2022
#2
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Check: The resulting polynomial 2x^2 + 4x + 2 is indeed the square of the binomial $$(\sqrt 2 x + \sqrt 2)^2$$

MaxWong  May 15, 2022