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 n?

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

Correct Answer: -3

Step 1: Identify the roots of the quadratic equation. The roots given are 1 and -3.
Step 2: Recall Vieta's formulas, which state that for a quadratic equation ax^2 + bx + c = 0, the product of the roots (r1 and r2) is equal to c/a.
Step 3: In our equation x^2 + mx + n = 0, the coefficient a is 1 (since it's x^2), and c is n.
Step 4: Calculate the product of the roots: 1 * (-3) = -3.
Step 5: According to Vieta's formulas, this product is equal to n. Therefore, n = -3.

Quadratic Equations – Understanding the properties of quadratic equations, specifically Vieta's formulas which relate the coefficients of the equation to the sums and products of its roots.
Roots of Quadratic Equations – Identifying and calculating the roots of a quadratic equation and how they relate to the coefficients.