If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value

If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of m?

If the quadratic equation x^2 + mx + n = 0 has roots 1 and -3, what is the value of m?

Correct Answer: 2

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.

Quadratic Equations – Understanding the standard form of quadratic equations and how to find coefficients from given roots.
Vieta's Formulas – Using Vieta's relations to relate the coefficients of a polynomial to sums and products of its roots.