If the quadratic equation x^2 + mx + n = 0 has roots 2 and -3, what is the value of m + n?
Practice Questions
1 question
Q1
If the quadratic equation x^2 + mx + n = 0 has roots 2 and -3, what is the value of m + n?
-1
5
1
3
Using Vieta's formulas, m = -(-1) = 1 and n = 2*(-3) = -6, thus m + n = 1 - 6 = -5.
Questions & Step-by-step Solutions
1 item
Q
Q: If the quadratic equation x^2 + mx + n = 0 has roots 2 and -3, what is the value of m + n?
Solution: Using Vieta's formulas, m = -(-1) = 1 and n = 2*(-3) = -6, thus m + n = 1 - 6 = -5.
Steps: 10
Step 1: Identify the roots of the quadratic equation, which are given as 2 and -3.
Step 2: Use Vieta's formulas, which tell us that for a quadratic equation of the form x^2 + mx + n = 0, the sum of the roots (2 + (-3)) is equal to -m.
Step 3: Calculate the sum of the roots: 2 + (-3) = -1.
Step 4: Set the sum of the roots equal to -m: -1 = -m.
Step 5: Solve for m: m = 1.
Step 6: Use Vieta's formulas again, which state that the product of the roots (2 * -3) is equal to n.
Step 7: Calculate the product of the roots: 2 * -3 = -6.
Step 8: Set the product of the roots equal to n: n = -6.
