If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the
Practice Questions
Q1
If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
7
12
10
8
Questions & Step-by-Step Solutions
If the roots of the quadratic equation x^2 + mx + n = 0 are 3 and 4, what is the value of m?
Correct Answer: -7
Step 1: Identify the roots of the quadratic equation. The roots given are 3 and 4.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -m/a. Here, a = 1 (since the equation is x^2 + mx + n = 0).
Step 3: Calculate the sum of the roots: 3 + 4 = 7.
Step 4: Set the sum of the roots equal to -m: 7 = -m.
Step 5: Solve for m by multiplying both sides by -1: m = -7.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Vieta's Formulas – The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a.
