What are the sum and product of the roots for the quadratic equation x^2 + 20x + 3 = 0?
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Answer: C. -20, 3
Explanation
For any standard quadratic equation written as ax squared plus bx plus c equals zero, the sum of roots is negative b over a. The product of the roots for a quadratic equation is given by the constant term c divided by the leading coefficient a. Applying these coefficients from x squared plus twenty x plus three equals zero gives a root sum of negative twenty and product of three. Vieta's formulas establish direct algebraic links between the coefficients of a polynomial and the sums and products of its roots. A quadratic equation is a second-order polynomial expression containing a variable raised to the power of two. The leading coefficient of a standard quadratic expression without an explicit multiplier is understood to be equal to one.
Option A incorrectly suggests a positive sum of ten, ignoring the negative sign associated with the linear coefficient b. Option B proposes a root sum of negative ten, which incorrectly halves the coefficient value from the equation. Option D suggests both a negative sum and negative product, violating the positive sign of the constant term c.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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