Question

If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?

• A. 5
• B. -5
• C. 6
• D. -6

Hint:

For a quadratic equation \( ax^2 + bx + c = 0 \), the sum of the roots is \( -\frac{b}{a} \).

Answer 1

The Correct Option is A

The quadratic equation is \( x^2 - 5x + 6 = 0 \). We know from Vieta's formulas that for a quadratic equation \( ax^2 + bx + c = 0 \), the sum of the roots \( p + q \) is given by \( -\frac{b}{a} \). For the equation \( x^2 - 5x + 6 = 0 \), we have \( a = 1 \), \( b = -5 \), and \( c = 6 \). Therefore: \[ p + q = -\frac{-5}{1} = 5 \] Thus, the value of \( p + q \) is 5. Therefore, the correct answer is option (1).