Question: If the quadratic equation x^2 + px + q = 0 has roots 2 and 3, what is the value of p?
Options:
-5
-6
-7
-8
Correct Answer: -5
Solution:
The sum of the roots is -p = 2 + 3 = 5, so p = -5.
If the quadratic equation x^2 + px + q = 0 has roots 2 and 3, what is the value
Practice Questions
Q1
If the quadratic equation x^2 + px + q = 0 has roots 2 and 3, what is the value of p?
-5
-6
-7
-8
Questions & Step-by-Step Solutions
If the quadratic equation x^2 + px + q = 0 has roots 2 and 3, what is the value of p?
Step 1: Identify the roots of the quadratic equation. The roots given are 2 and 3.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -p. This means -p = root1 + root2.
Step 3: Calculate the sum of the roots: 2 + 3 = 5.
Step 4: Set up the equation: -p = 5.
Step 5: Solve for p by multiplying both sides by -1: p = -5.
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 how to calculate the sum and product of the roots to find the coefficients.
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