If the equation x^2 + 5x + 6 = 0 has roots α and β, what is the value of αβ?
Practice Questions
Q1
If the equation x^2 + 5x + 6 = 0 has roots α and β, what is the value of αβ?
6
5
4
3
Questions & Step-by-Step Solutions
If the equation x^2 + 5x + 6 = 0 has roots α and β, what is the value of αβ?
Step 1: Identify the equation given, which is x^2 + 5x + 6 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c = 0.
Step 3: Identify the coefficients: a = 1, b = 5, and c = 6.
Step 4: Understand that the product of the roots (αβ) of a quadratic equation can be found using the formula αβ = c/a.
Step 5: Substitute the values of c and a into the formula: αβ = 6/1.
Step 6: Calculate the result: αβ = 6.
Quadratic Equations – Understanding the properties of quadratic equations, specifically Vieta's formulas which relate the coefficients of the polynomial to sums and products of its roots.
Roots of Polynomials – Identifying and calculating the roots of a quadratic equation and their relationships.
