If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?

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Question: If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?

Options:

Correct Answer: 4

Solution:

Substituting x = 2 into the equation gives 2^2 - 3*2 + p = 0 => 4 - 6 + p = 0 => p = 2.

If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?

If one root of the equation x^2 - 3x + p = 0 is 2, what is the value of p?

Step 1: Start with the equation x^2 - 3x + p = 0.
Step 2: We know that one root of the equation is 2. This means we can substitute x with 2.
Step 3: Substitute x = 2 into the equation: 2^2 - 3*2 + p = 0.
Step 4: Calculate 2^2, which is 4.
Step 5: Calculate -3*2, which is -6.
Step 6: Now the equation looks like this: 4 - 6 + p = 0.
Step 7: Simplify 4 - 6, which equals -2. So now we have -2 + p = 0.
Step 8: To find p, add 2 to both sides of the equation: p = 2.

Quadratic Equations – Understanding how to substitute values into a quadratic equation to find unknown coefficients.
Roots of Equations – Identifying and using the roots of a quadratic equation to solve for parameters.