What are the roots of the quadratic equation 3x2 – 12x + 10 = 0?
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Answer: D. irrational and unequal
Explanation
Calculating the discriminant for three x squared minus twelve x plus ten equals fourteen minus one twenty. The resulting discriminant value of twenty four is positive but fails to form a perfect square. Quadratic equations with positive non square discriminants possess roots that are irrational and unequal. The discriminant formula b squared minus four a c determines the nature of quadratic equation roots. Roots are rational and unequal when the discriminant evaluates to a positive perfect square number. Roots are irrational and unequal when the discriminant is positive but not a perfect square.
Physics simulations use quadratic equations to model projectile motion and trajectory intersection points. Engineering design calculations rely on root classifications to determine stability thresholds in structures. Algebraic analysis helps mathematicians categorize polynomial behavior without explicitly solving for every root. Option a requires the discriminant to be a positive perfect square to yield rational roots. Option b applies only when the discriminant evaluates to a negative numerical value. Option c occurs exclusively when the discriminant equals zero resulting in repeated roots.
- Subject
- Mathematics
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- Mathematics
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- Difficulty
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