List of top Mathematics Questions on Quadratic Equations asked in TS EAMCET

If all roots of \[ x^5-3x^4+2x^3-3x^2+5x-2=0 \] are increased by real value h so that term containing \(x^3\) vanishes in transformed equation and h is integer, then h=

If \(\alpha\in R\) and equation \[ (x-\alpha)(x-3)+1=0 \] has equal roots, then sum of squares of all values of \(\alpha\) is

Two real roots of \[ 3x^4+ax^3+55x^2-52x+12=0 \] are positive and equal. Product of other two roots is 1. If roots belong to natural numbers then \[ a\beta-a+\frac{\gamma}{\delta}= \]

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - Px^2 + Qx - R = 0 \) and \( (\alpha-2)^2, (\beta-2)^2, (\gamma-2)^2 \) are the roots of the equation \( x^3 - 5x^2 + 4x = 0 \), then the possible least value of \( P+Q+R \) is

The number of all common roots of the equation \( x^4 - 10x^3 + 37x^2 - 60x + 36 = 0 \) and the transformed equation of it obtained by increasing any two distinct roots of it by 1, keeping the other two roots fixed, is

If the equation \( x^2 - 3ax + a^2 - 2a - K = 0 \) has different real roots for every rational number \( a \), then \( K \) lies in the interval