Set 1: Quadratic Equations

Choice A is correct. Choice A is the correct answer. Method 1: Factoring If roots are 3 and -5, factors are $(x - 3)$ and $(x + 5)$. Multiply: $(x - 3)(x + 5) = x^2 + 5 x - 3 x - 15 = x^2 + 2 x - 15$. Method 2: Vieta's Formulas Sum = $3+ (-5) = -2$. Product = $3(-5) = -15$. Equation: $x^2 - (Sum)x + Product = 0 \Rightarrow x^2 - (-2)x - 15 = 0 \Rightarrow x^2 + 2 x - 15 = 0$. Choice B is incorrect because sum is -2, so coefficient should be +2. Choice C is incorrect because product is -15. Choice D is incorrect because it swaps sum and product.