List of top Quantitative Aptitude Questions on Polynomials asked in CAT

Consider the curves: \[ y = 2x^3 + 3x^2 + 4, y = 3x^2 - 2x + 8 \] How many times do they intersect for \( -3 \leq x \leq 2 \)?

Suppose \(n\) is an integer such that the sum of digits of \(n\) is 2, and \(10^n<n<10^{n+1}\). The number of different values of \(n\) is

If \(f(x) = x^3 - 4x + p\), and \(f(0)\) and \(f(1)\) are of opposite signs, then which of the following is necessarily true?

If (Ax + By - Cz)² = 4x²+ 3y²+ 2z²+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.