Math Problem Statement
If the sum and product of the roots of a quadratic equation are 8 and 15 respectively, then the equation is: (a) x2 − 8x + 15 = 0 (b) x2 + 8x + 15 = 0 (c) x2 − 15x + 8 = 0 (d) x2 + 15x − 8 = 0
Solution
The general form of a quadratic equation is:
From Vieta's formulas, for a quadratic equation , the sum of the roots and the product of the roots are given by:
For the given quadratic equation:
- Sum of the roots = 8
- Product of the roots = 15
Thus, we have:
Comparing with Vieta's formulas, we know:
Assuming (since the coefficient of is not specified), we get:
Thus, the quadratic equation is:
Therefore, the correct answer is:
(a)
Would you like a detailed explanation or have any other questions on this topic? Here are a few related questions for you:
- How can you use Vieta's formulas to find the roots of a quadratic equation?
- What happens to the quadratic equation if the product of the roots is negative?
- Can you derive the quadratic equation if the roots are given directly?
- How can you calculate the discriminant of a quadratic equation from the sum and product of its roots?
- What is the relationship between the sum and product of the roots and the vertex of the quadratic function?
Tip: Always remember that the sum and product of the roots can give you quick insights into the structure of a quadratic equation!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Vieta's Formulas
Formulas
r1 + r2 = -b/a
r1 * r2 = c/a
Theorems
Vieta's Formulas
Suitable Grade Level
Grades 8-10