Product Of Roots Of Quadratic Equation Calculator

Product Of Roots Formula:

\[ P(x_1 \times x_2) = \frac{c}{a} \]

Product Of Roots:

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1. What is the Product Of Roots of Quadratic Equation?

The Product of Roots of a quadratic equation is the product of the values of the variables x₁ and x₂ that satisfy the given quadratic equation f(x). For a quadratic equation in the form ax² + bx + c = 0, the product of roots is given by c/a.

2. How Does the Calculator Work?

The calculator uses the Product of Roots formula:

\[ P(x_1 \times x_2) = \frac{c}{a} \]

Where:

\( P(x_1 \times x_2) \) — Product of Roots
\( a \) — Numerical coefficient of x² term
\( c \) — Constant term of the quadratic equation

Explanation: The formula shows that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of the x² term.

3. Importance of Product Of Roots Calculation

Details: Calculating the product of roots is essential in algebra for understanding the relationship between the coefficients and roots of quadratic equations. It helps in solving various mathematical problems and verifying solutions.

4. Using the Calculator

Tips: Enter the numerical coefficient a (coefficient of x²) and numerical coefficient c (constant term) of the quadratic equation. The coefficient a must not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if the coefficient a is zero?
A: If a = 0, the equation is not quadratic but linear. The product of roots formula only applies to quadratic equations where a ≠ 0.

Q2: How is this related to the sum of roots?
A: For a quadratic equation ax² + bx + c = 0, the sum of roots is -b/a and the product of roots is c/a.

Q3: Can this formula be used for complex roots?
A: Yes, the product of roots formula works for both real and complex roots of quadratic equations.

Q4: What are some practical applications of this formula?
A: This formula is used in solving systems of equations, optimization problems, and in various engineering and physics applications involving quadratic relationships.

Q5: How does this relate to Vieta's formulas?
A: The product of roots formula is part of Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.