Find the quadratic equation with one root 3 and other root 1/3 ?
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A. 3x² - 10x + 3 = 0
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B. 3x² - 8x - 3 = 0
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C. 3x² + 10x + 3 = 0
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D. 3x² + 8x - 3 = 0
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E. None
Reveal answer
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A
Correct answer
Explanation
Roots are 3 and 1/3. Sum = 3 + 1/3 = 10/3. Product = 3 * 1/3 = 1. Equation is x^2 - (sum)x + product = 0. x^2 - (10/3)x + 1 = 0. Multiply by 3: 3x^2 - 10x + 3 = 0.
AI explanation
Using the formula for forming a quadratic equation from its roots, x^2 - (sum of roots)x + (product of roots) = 0. The sum of the roots 3 and 1/3 is 10/3, and their product is 1. Substituting these values gives x^2 - (10/3)x + 1 = 0, and multiplying the entire equation by 3 yields 3x^2 - 10x + 3 = 0.