List of top Quantitative Aptitude Questions on Quadratic Equation

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

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 \(a\).

Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the orginal quadratic equation?

What is the number of distinct terms in the expansion of $(x + y + z )25$ ?

If p, q, r and s are four positive integers such that pqrs = 1, what is the minimum value of (2 + p)(3 + q)(4 + r)(5 + s)?

Given quadratic equation is x² - |x|-30 = 0. Then which of the following statements is/are incorrect?

Given quadratic equation is \(x^2-|x|-30=0 . \)Then which of the following statements is/are incorrect?