If one root of the equation x² - 7x + p = 0 is 3, what is the value of p? (2020)

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Question: If one root of the equation x² - 7x + p = 0 is 3, what is the value of p? (2020)

Options:

Correct Answer: 9

Exam Year: 2020

Solution:

Using the root, substitute x = 3: 3² - 7*3 + p = 0, which gives p = 6.

If one root of the equation x² - 7x + p = 0 is 3, what is the value of p? (2020)

If one root of the equation x² - 7x + p = 0 is 3, what is the value of p? (2020)

Step 1: Start with the equation x² - 7x + p = 0.
Step 2: We know that one root of the equation is 3. This means that if we substitute x with 3, the equation should equal 0.
Step 3: Substitute x = 3 into the equation: 3² - 7*3 + p = 0.
Step 4: Calculate 3², which is 9.
Step 5: Calculate 7*3, which is 21.
Step 6: Now, rewrite the equation with these values: 9 - 21 + p = 0.
Step 7: Simplify the left side: 9 - 21 equals -12, so we have -12 + p = 0.
Step 8: To find p, add 12 to both sides of the equation: p = 12.
Step 9: Therefore, the value of p is 12.

Quadratic Equations – Understanding how to substitute a known root into a quadratic equation to find an unknown coefficient.
Substitution Method – Using substitution to simplify and solve for unknown variables in equations.