List of top Quantitative Aptitude Questions on Quadratic Equation asked in CAT

Let \(x, y, z\) be real numbers such that \(4(x^2 + y^2 + z^2) = a\) and \(4(x - y - z) = 3 + a\), then find the value of \(a\).

The roots \(\alpha\), \(\beta\) of the equation \(3x^2 + \lambda x - 1 = 0\), satisfy \( \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15 \). The value of \( (\alpha^3 + \beta^3)^2 \) is

Suppose one of the roots of the equation \(a x^2 - b x + c = 0 \) is \( 2 + \sqrt{3}\), where a, b and c are rational numbers and \(a ≠ 0\). If \(b = c^3\) then |a| equals