Difficulty: Medium One way to do this problem is to think about the properties of roots. Suppose the two roots of a quadratic equation are a and b. Then the quadratic equation can be written in factored form as (x minus a) times (x minus b) = 0. The sum of the roots is a + b, and the product is a times b. Note that(x minus a) times (x minus b) = x^2 minus ((a + b) times x) + (a times b). In this question the sum of the roots is 5 and the product is negative 6. Therefore, (a + b) = 5 and a times b = negative 6. The equation could be x^2 minus (5 times x) minus 6 = 0, which is choice B. Note that the roots of this equation are 6 and negative 1. Their sum is 5 and their product is negative 6. If you know these properties of roots, you do not need to factor all of the equations to find the one that fits the given conditions.
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