If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value
Practice Questions
Q1
If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?
0
6
-6
9
Questions & Step-by-Step Solutions
If the quadratic equation x^2 + bx + 9 = 0 has roots 3 and -3, what is the value of b?
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and -3.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -b/a. Here, a = 1 (since the equation is x^2 + bx + 9 = 0).
Step 3: Calculate the sum of the roots: 3 + (-3) = 0.
Step 4: Set the sum of the roots equal to -b/a. Since a = 1, this simplifies to 0 = -b/1, or 0 = -b.
Step 5: Solve for b. If 0 = -b, then b = 0.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Roots of Quadratic Equations – Identifying and calculating the sum and product of the roots of a quadratic equation.
