Question: If the roots of the equation x² - 6x + p = 0 are 2 and 4, what is the value of p? (2023)
Options:
8
12
6
10
Correct Answer: 12
Exam Year: 2023
Solution:
The product of the roots gives p = 2 * 4 = 8.
If the roots of the equation x² - 6x + p = 0 are 2 and 4, what is the value of p
Practice Questions
Q1
If the roots of the equation x² - 6x + p = 0 are 2 and 4, what is the value of p? (2023)
8
12
6
10
Questions & Step-by-Step Solutions
If the roots of the equation x² - 6x + p = 0 are 2 and 4, what is the value of p? (2023)
Step 1: Identify the equation given, which is x² - 6x + p = 0.
Step 2: Recognize that the roots of the equation are given as 2 and 4.
Step 3: Use the property of quadratic equations that states the product of the roots (r1 * r2) is equal to p.
Step 4: Calculate the product of the roots: 2 * 4.
Step 5: Perform the multiplication: 2 * 4 = 8.
Step 6: Conclude that the value of p is 8.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Roots of Equations – Identifying and applying the roots of a quadratic equation to find unknown coefficients.
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