Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.3 Junior Find the answer

If $x=1$ is a solution of the equation $x^{2} + ax + 1 = 0$ , what is the value of $a$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $x=1$ is a solution of the equation $x^{2} + ax + 1 = 0$ , then $1^{2} + a(1) + 1 = 0$ or $2 + a = 0$ and so $a = -2$ .

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