JAMB Mathematics 2014 Paper

Concept:The binary operation tells us to raise the first number to the power of the second number.So we substitute the given condition into the operation and solve the resulting quadratic equation.Explanation:The operation is defined as $x \ast y = x^y$.We are told that $x \ast 2 = 12 - x$.Put $y = 2$ into the definition of the operation.This gives $x \ast 2 = x^2$.Since both expressions equal $x \ast 2$, we equate them.So $x^2 = 12 - x$.Rearrange all terms to one side of the equation.We obtain $x^2 + x - 12 = 0$.Now factorise the quadratic expression.We need two numbers whose product is $-12$ and whose sum is $1$.These numbers are $4$ and $-3$.So we rewrite the middle term as $4x - 3x$.This gives $x^2 + 4x - 3x - 12 = 0$.Group the terms into pairs: $x(x + 4) - 3(x + 4) = 0$.Factor out the common bracket to get $(x - 3)(x + 4) = 0$.Set each factor equal to zero: $x - 3 = 0$ or $x + 4 = 0$.Solving these equations gives $x = 3$ or $x = -4$.Answer:The possible values are $x = 3$ or $x = -4$.