Question

A quadratic equation whose roots are \[ \alpha, \beta \] can be written as:

Options

• \( x^{2} + (\alpha + \beta)x + \alpha\beta = 0 \)

• \( x^{2} + (\alpha + \beta)x - \alpha\beta = 0 \)

• \( x^{2} - (\alpha + \beta)x - \alpha\beta = 0 \)

• \( x^{2} - (\alpha + \beta)x + \alpha\beta = 0 \)

Answer 1

A quadratic with roots \[ \alpha, \beta \] is \[ x^{2} - (\alpha + \beta)x + \alpha\beta = 0 \]. The coefficient of \( x \) is the negative of the sum of the roots, and the constant term is the product of the roots.