Question

If a quadratic equation \[ ax^{2} + bx + c = 0 \] has roots \[ \alpha = 2 \] and \[ \beta = 3 \], which equation has exactly these roots?

Options

• \( x^{2} - 5x + 6 = 0 \)

• \( x^{2} - 5x - 6 = 0 \)

• \( x^{2} - 6x + 5 = 0 \)

• \( x^{2} + 5x + 6 = 0 \)

Answer 1

Using \[ x^{2} - (\alpha + \beta)x + \alpha\beta = 0 \] with \( \alpha + \beta = 2 + 3 = 5 \) and \( \alpha\beta = 2 \times 3 = 6 \), the equation becomes \[ x^{2} - 5x + 6 = 0 \].