If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of m?
Practice Questions
1 question
Q1
If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of m?
2
-2
4
-4
Using Vieta's formulas, m = -(1 + (-3)) = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of m?
Solution: Using Vieta's formulas, m = -(1 + (-3)) = 2.
Steps: 5
Step 1: Understand that the roots of the quadratic equation are the values of x that make the equation equal to zero. In this case, the roots are 1 and -3.
Step 2: Recall Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots. For a quadratic equation of the form x^2 + mx + n = 0, the sum of the roots is -m.
Step 3: Calculate the sum of the roots. Here, the roots are 1 and -3. So, the sum is 1 + (-3) = 1 - 3 = -2.
Step 4: According to Vieta's formulas, the sum of the roots (1 + (-3)) is equal to -m. Therefore, we have -m = -2.
Step 5: To find m, we can multiply both sides of the equation by -1. This gives us m = 2.
