If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of

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Question: If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?

Options:

Correct Answer: 5

Solution:

According to Vieta\'s formulas, the sum of the roots r1 + r2 of the polynomial x^2 - 5x + 6 is equal to the coefficient of x (which is -(-5)) = 5.

If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?

If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?

Step 1: Identify the polynomial given in the question, which is P(x) = x^2 - 5x + 6.
Step 2: Recognize that this is a quadratic polynomial of the form ax^2 + bx + c, where a = 1, b = -5, and c = 6.
Step 3: Recall Vieta's formulas, which state that for a quadratic polynomial ax^2 + bx + c, the sum of the roots (r1 + r2) is equal to -b/a.
Step 4: In our polynomial, b is -5 and a is 1.
Step 5: Substitute the values into the formula: r1 + r2 = -(-5)/1.
Step 6: Simplify the expression: r1 + r2 = 5/1 = 5.
Step 7: Conclude that the value of r1 + r2 is 5.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
Quadratic Polynomials – Understanding the standard form of a quadratic polynomial and how to identify its coefficients.