List of top Quantitative Aptitude Questions on Quadratic Equations asked in NPAT

If \( -4 \) is a root of the equation \( x^2 + ax - 4 = 0 \) and the equation \( x^2 + ax + b = 0 \) has equal roots, then what will be the value of \( \sqrt{a^2 + b^2} \)?
If \( \alpha \) and \( \beta \) are the roots of the equation \( 2x^2 + 5x + k = 0 \), and \( 4(\alpha^2 + \beta^2 + \alpha\beta) = 23 \), then which of the following is true?
If the roots of the equation \(x^2 - 2(1+3k)x + 7(3+2k) = 0\) are equal, where \(k<0\), then which of the following is true?
If the roots of the equation \(x^2 - 2(1+3k)x + 7(3+2k) = 0\) are equal, where \(k<0\), then which of the following is true?
Which of the following statements is true about the solutions of the equation \(\lvert x^2 - 5x \rvert = 6\)?
Which of the following statements is true about the solutions of the equation \(\lvert x^2 - 5x \rvert = 6\)?
If the equations \( x^2 + px + 12 = 0 \), \( x^2 + qx + 15 = 0 \), and \( x^2 + (p+q)x + 36 = 0 \) have a common positive root, then what is the value of \( (2p - q) \)?