The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?

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Question: The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?

Options:

Correct Answer: 3/2

Solution:

Using Vieta\'s formulas, the sum of the roots is -(-3)/2 = 3/2.

The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?

The sum of the roots of the equation 2x^2 - 3x + 1 = 0 is equal to what?

Step 1: Identify the equation given, which is 2x^2 - 3x + 1 = 0.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c = 0, where a = 2, b = -3, and c = 1.
Step 3: Recall Vieta's formulas, which tell us that for a quadratic equation, the sum of the roots (let's call them r1 and r2) is given by -b/a.
Step 4: Substitute the values of b and a into the formula: -(-3)/2.
Step 5: Simplify the expression: -(-3) becomes 3, so we have 3/2.
Step 6: Conclude that the sum of the roots of the equation is 3/2.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.