If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of

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Question: If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of n? (2022)

Options:

Correct Answer: 12

Exam Year: 2022

Solution:

Using Vieta\'s formulas, n = 3 * 4 = 12.

If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of n? (2022)

If the roots of the equation x^2 + mx + n = 0 are 3 and 4, what is the value of n? (2022)

Step 1: Understand that the equation x^2 + mx + n = 0 is a quadratic equation.
Step 2: Recognize that the roots of the equation are given as 3 and 4.
Step 3: Recall Vieta's formulas, which tell us that for a quadratic equation ax^2 + bx + c = 0, the product of the roots (r1 and r2) is equal to c/a.
Step 4: In our equation, a = 1, b = m, and c = n.
Step 5: Since the roots are 3 and 4, we can find n by multiplying the roots: n = 3 * 4.
Step 6: Calculate the product: 3 * 4 = 12.
Step 7: Conclude that the value of n is 12.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.