WAEC Mathematics 2011 Paper

Concept:A quadratic equation can be solved by factorising it into two linear factors and then setting each factor equal to zero.Explanation:The given equation is $x^2 + 7x + 10 = 0$.We need two numbers whose sum is $7$ and whose product is $10$.These numbers are $5$ and $2$, because $5 + 2 = 7$ and $5 \times 2 = 10$.So, split the middle term: $x^2 + 5x + 2x + 10 = 0$.Group the terms: $x(x + 5) + 2(x + 5) = 0$.Factor out $(x + 5)$: $(x + 2)(x + 5) = 0$.Now set each factor to zero: $x + 2 = 0$ or $x + 5 = 0$.This gives $x = -2$ or $x = -5$.The two solutions are $-2$ and $-5$.The smaller value among these is $-5$.Answer:The smaller value of $x$ is $-5$, which is option A.