What is the product of the roots of the polynomial P(x) = x^2 - 7x + 10?

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Question: What is the product of the roots of the polynomial P(x) = x^2 - 7x + 10?

Options:

Correct Answer: 10

Solution:

The product of the roots of a quadratic polynomial ax^2 + bx + c is given by c/a, which is 10/1 = 10.

What is the product of the roots of the polynomial P(x) = x^2 - 7x + 10?

What is the product of the roots of the polynomial P(x) = x^2 - 7x + 10?

Step 1: Identify the polynomial given in the question, which is P(x) = x^2 - 7x + 10.
Step 2: Recognize that this is a quadratic polynomial in the form ax^2 + bx + c.
Step 3: Identify the coefficients a, b, and c from the polynomial. Here, a = 1, b = -7, and c = 10.
Step 4: Use the formula for the product of the roots of a quadratic polynomial, which is given by c/a.
Step 5: Substitute the values of c and a into the formula: c/a = 10/1.
Step 6: Calculate the result: 10/1 = 10.
Step 7: Conclude that the product of the roots of the polynomial P(x) is 10.

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