The product of the roots of the equation 2x^2 - 4x + 2 = 0 is equal to what?

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Question: The product of the roots of the equation 2x^2 - 4x + 2 = 0 is equal to what?

Options:

Correct Answer: 1

Solution:

The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 2 and a = 2, so the product is 2/2 = 1.

The product of the roots of the equation 2x^2 - 4x + 2 = 0 is equal to what?

The product of the roots of the equation 2x^2 - 4x + 2 = 0 is equal to what?

Step 1: Identify the coefficients in the quadratic equation 2x^2 - 4x + 2 = 0. Here, a = 2, b = -4, and c = 2.
Step 2: Recall the formula for the product of the roots of a quadratic equation, which is given by c/a.
Step 3: Substitute the values of c and a into the formula. Here, c = 2 and a = 2.
Step 4: Calculate the product of the roots: 2 (value of c) divided by 2 (value of a) equals 1.
Step 5: Conclude that the product of the roots of the equation is 1.

Quadratic Equations – Understanding the standard form of a quadratic equation and the relationship between its coefficients and roots.
Product of Roots – Applying the formula for the product of the roots of a quadratic equation, which is given by c/a.