List of top Quantitative Ability and Data Interpretation Questions on Quadratic Equation

If the roots of the equation px² + x + r = 0 are reciprocal to each other, then which one of the following is correct?

If $x^2-3x+2$ is a factor of $x^4-px+q$, then $(p,q)$ = 

Which of the following statements regarding quadratic equations are true?
(A) Solution set for the equation 6x²-5x=4 is $\{-\frac{1}{2},\frac{4}{3}\}$.
(B) The nature of the roots of the equation 9x²+6x+1=0 is equal, real and rational.
(C) If one root of 4x²-3x+K=0 is 3 times the other, then $K=\frac{27}{256}$
Choose the correct answer from the options given below:

If f(x) = $x$³ −4$x$ $+$P and f(0) and f(1) are of opposite signs, Which one of the following is necessarily true?