Question: If one root of the equation x^2 + px + q = 0 is 3, what is the value of p if the other root is 1?
Options:
-4
-6
4
6
Correct Answer: -6
Solution:
Using the sum of the roots, p = -(3 + 1) = -4. The product of the roots gives q = 3 * 1 = 3.
If one root of the equation x^2 + px + q = 0 is 3, what is the value of p if the
Practice Questions
Q1
If one root of the equation x^2 + px + q = 0 is 3, what is the value of p if the other root is 1?
-4
-6
4
6
Questions & Step-by-Step Solutions
If one root of the equation x^2 + px + q = 0 is 3, what is the value of p if the other root is 1?
Step 1: Identify the given roots of the equation. We know one root is 3 and the other root is 1.
Step 2: Use the formula for the sum of the roots of a quadratic equation, which is -p. The sum of the roots (3 + 1) is 4.
Step 3: Set up the equation for the sum of the roots: -p = 4.
Step 4: Solve for p by multiplying both sides by -1: p = -4.
Step 5: To find q, use the product of the roots formula, which is q = root1 * root2. Here, q = 3 * 1 = 3.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Sum and Product of Roots – Applying the formulas for the sum and product of the roots of a quadratic equation to find unknown coefficients.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
