Jerry F. answered • 02/10/23
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If the solutions to the quadratic equation are 3 and -2, then it must be true that x - 3 = 0 and x + 2 = 0.
Since each of these expressions is zero, their product must also be zero.
(x - 3)(x + 2) = 0
Expand to get x2 - 3x +2x - 6 = 0 → x2 - x - 6 = 0.
To satisfy the second condition, multiply the equation by 2: 2x2 2x -12 = 0. Since the right side of the equation is zero, multiplying it by 2 still yields zero.
Jerry F.
This question uses the zero product rule: if the product of two terms is zero, then either of the single terms must be individually zero.02/10/23