Find a quadratic equation formed by using the equations x - y = 7 and xy = 18.
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x2 - 7x - 18 = 0
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x2 - 18x - 7 = 0
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x2 + 7x - 18 = 0
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x2 + 18x + 7 = 0
If the roots of a quadratic equation are x and y, the equation is t^2 - (sum)t + (product) = 0. Here, x - y = 7 and xy = 18. This implies x and y are roots of t^2 - (x+y)t + xy = 0. However, the question asks for an equation using x - y = 7 and xy = 18. If we treat x as the variable, the equation x^2 - 7x - 18 = 0 has roots 9 and -2, where 9 - (-2) = 11 (not 7) and 9 * -2 = -18. If we use x^2 - 7x - 18 = 0, the roots are 9 and -2. The difference is 11. If the equation is x^2 - 7x - 18 = 0, it matches the form provided in option A.
From the first equation x - y = 7, we can express y as x - 7. Substituting this into the second equation xy = 18 gives x(x - 7) = 18. Expanding the product yields x2 - 7x = 18. Moving all terms to the left side results in the quadratic equation x2 - 7x - 18 = 0.