A binary operation * is defined by x * y = xy. If x * 2 = 12 - x, find the possible values of x

Analyze the question

The operation is defined by x * y = xy, so we replace y with 2 and then use the condition x * 2 = 12 - x.

Concept

A binary operation is just a rule for combining two numbers. Substitute carefully into the rule as given.

Solution (as written)

x * 2 = x · 2 = 2x

Setting 2x = 12 - x gives 3x = 12, so x = 4 (only one value).

That gives a single value, not two, so the question as typed doesn't match the options. The original JAMB question almost certainly defines the operation as x * y = x²y, or something like x * y = xʸ, so that a quadratic appears. Let's test the likely versions.

Version 1: x * y = x^y (power)

x * 2 = x² = 12 - x x² + x - 12 = 0 (x + 4)(x - 3) = 0 x = 3 or x = -4

This matches option B exactly, and the numbers factor nicely, which strongly suggests this is the intended question (the "xy" is most likely x^y, with the superscript lost in formatting).

Check:

• x = 3: 3² = 9 and 12 - 3 = 9 ✓
• x = -4: (-4)² = 16 and 12 - (-4) = 16 ✓

Note: If the rule is literally x * y = xy (ordinary multiplication), the only solution is x = 4, which isn't paired with a second value in any option. So the answer matches the official key only under the x^y interpretation, which is almost certainly what was intended.

Answer: B (3, -4)

Tip: When a binary operation question asks for "possible values" (plural), expect a quadratic. Substitute into the rule, move everything to one side, and factorise. Always check the original wording of the operation, since the exponent is easy to lose when copying.