defence exam Coast Guard Navik GD (General Duty) 02/2025 Mock Test Series Mathematics Quadratic Equations
Let \(p\) and \(q\) be real numbers such that \(p \neq 0, p^{3} \neq q\) and \(p^{3} \neq -q\). If \(\alpha\) and \(\beta\) are non-zero complex numbers satisfying \(\alpha + \beta = -p\) and \(\alpha^{3} + \beta^{3} = q\), then a quadratic equation having \(\dfrac{\alpha}{\beta}\) and \(\dfrac{\beta}{\alpha}\) as its roots is
1
\((p^{3} + q)x^{2} - (p^{3} + 2q)x + (p^{3} + q) = 0\)
2
\((p^{3} + q)x^{2} - (p^{3} - 2q)x + (p^{3} + q) = 0\)
3
\((p^{3} - q)x^{2} - (5p^{3} - 2q)x + (p^{3} - q) = 0\)
4
\((p^{3} - q)x^{2} - (5p^{3} + 2q)x + (p^{3} - q) = 0\)