Question

The set of real numbers which satisfy the equation \( x^2 - 5x + 6 = 0 \) is:

• A. (2,3)
• B. (-2,-3)
• C. (5,1)
• D. (-2,3)

Hint:

To solve a quadratic equation of the form \( ax^2 + bx + c = 0 \), factorize if possible or use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Answer 1

The Correct Option is A

Given quadratic equation: \[ x^2 - 5x + 6 = 0 \] Factorizing: \[ x^2 - 2x - 3x + 6 = 0 \] \[ x(x - 2) - 3(x - 2) = 0 \] \[ (x - 2)(x - 3) = 0 \] Setting each factor to zero: \[ x - 2 = 0 \Rightarrow x = 2 \] \[ x - 3 = 0 \Rightarrow x = 3 \]
Thus, the solution set is \( \{2,3\} \).