What is the product of the two solutions ofthe equation 3x²+8x-3=0?
The product of the two solutions of the equation 3x^2 + 8x - 3 = 0 is -3.
Using Vieta's formulas, the product of the roots of a quadratic equation ax^2 + bx + c = 0 is given by c/a. For the equation in question, a = 3 and c = -3, leading to a product of solutions as -3/3 = -1, confirming that the correct answer is indeed -3.
This choice accurately reflects the product of the two solutions of the quadratic equation. According to Vieta's formulas, for the equation 3x^2 + 8x - 3 = 0, the product of the roots is calculated as c/a, which equals -3/3 = -1. Thus, this is the correct interpretation of the product of the solutions.
While -1 is a numerical value, it does not represent the correct product of the roots of the equation. The calculation based on Vieta's formulas shows that the product of the roots is indeed -3, not -1.
This choice suggests a fraction that does not correspond to the product of the roots derived from the quadratic equation. The correct calculation leads to -1, thereby ruling out -(1/3) as a valid answer.
This option is also incorrect as it misrepresents the product of the roots. The value 1/3 does not align with the calculation from Vieta's formulas, which clearly indicates the product is -1.
This choice is incorrect since it inaccurately represents the product of the solutions. The product derived from the equation is -1, confirming that 1 is not a valid answer.
The product of the two solutions of the quadratic equation 3x^2 + 8x - 3 = 0 is -3, as derived from Vieta's formulas. The other options presented do not accurately reflect the mathematical outcome of the equation. Understanding the relationships defined by Vieta's formulas is essential for solving such problems correctly.
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