If the roots of the equation x² + mx + n = 0 are 1 and -1, find m and n. (2020)

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Question: If the roots of the equation x² + mx + n = 0 are 1 and -1, find m and n. (2020)

Options:

Correct Answer: 0, 1

Exam Year: 2020

Solution:

The sum of the roots is 0 (m = 0) and the product is -1 (n = 1).

If the roots of the equation x² + mx + n = 0 are 1 and -1, find m and n. (2020)

If the roots of the equation x² + mx + n = 0 are 1 and -1, find m and n. (2020)

Step 1: Identify the given quadratic equation, which is x² + mx + n = 0.
Step 2: Recognize that the roots of the equation are given as 1 and -1.
Step 3: Use the formula for the sum of the roots, which is -m. Since the roots are 1 and -1, their sum is 1 + (-1) = 0.
Step 4: Set the sum of the roots equal to -m: 0 = -m. This means m = 0.
Step 5: Use the formula for the product of the roots, which is n. The product of the roots 1 and -1 is 1 * (-1) = -1.
Step 6: Set the product of the roots equal to n: n = -1.

Roots of Quadratic Equations – Understanding how to find the coefficients of a quadratic equation using the sum and product of its roots.
Vieta's Formulas – Applying Vieta's formulas to relate the coefficients of a polynomial to sums and products of its roots.