What is the sum of the roots of log₂(x² − x − 10) = 1?

Question

Solve log₂(x² − x − 10) = 1. If there is more than one root, give their sum.

Answer

The roots are 4 and −3. Their sum is 1.

Explanation

By the definition of a logarithm:

log₂(x² − x − 10) = 1 ⇒ x² − x − 10 = 2.

This gives:

x² − x − 12 = 0 ⇒ (x − 4)(x + 3) = 0.

Thus x₁ = 4 and x₂ = −3. For both roots, the logarithm's argument equals 2, satisfying the requirement that it be positive.

The requested sum is 4 + (−3) = 1.