If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?
Practice Questions
1 question
Q1
If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?
5
-5
6
-6
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.
Questions & Step-by-step Solutions
1 item
Q
Q: If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?
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.
Steps: 7
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.
