Question

The sum of two numbers is 11 and their product is 30, then the numbers are:

• A. 8, 3
• B. 7, 4
• C. 6, 5
• D. 9, 2

Hint:

For problems involving the sum and product of two numbers, use a quadratic equation to find the solutions.

Answer 1

The Correct Option is C

Let the two numbers be \( x \) and \( y \). We are given the system of equations: \[ x + y = 11 \quad \text{and} \quad x \times y = 30 \] We can solve these equations using the quadratic equation. Substitute \( y = 11 - x \) into the second equation: \[ x \times (11 - x) = 30 \] \[ x^2 - 11x + 30 = 0 \] Factoring the quadratic equation: \[ (x - 6)(x - 5) = 0 \] Thus, \( x = 6 \) and \( y = 5 \) (or vice versa). Therefore, the correct answer is \( 6, 5 \).