List of top Mathematics Questions on Polynomials asked in AP EAPCET

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - 3x + 1 = 0 \), then \( \frac{\alpha}{1-\alpha} + \frac{\beta}{1-\beta} + \frac{\gamma}{1-\gamma} = \)

If \( x^5 + ax^4 + bx^3 + cx^2 + 5x + d = 0 \) is an odd order reciprocal equation of second type and \( \frac{1+\sqrt{3}i}{2} \) is a root, then \( b-c = \)

If \(5\) is the remainder when \[ 2x^5+kx^4+5x^3-3x^2+2x-1 \] is divided by \[ x^2+x+1, \] then the quotient is:

If \(\alpha,\beta,\gamma,\delta\) are the roots of the equation \[ x^4+x^3-x-1=0, \] then \[ \alpha^3+\beta^3+\gamma^3+\delta^3= \]

If \( x^{5}+ax^{4}+b death^{3}+cx^{2}+5x+e=0 \) is a reciprocal equation of second kind such that \( a+b=4 \) then the number of complex roots of this equation is

If \(\alpha\) is a root of the equation \[ x^4-4x^3+16x-16=0 \] of multiplicity \(m\), then \[ m^2-4m+2= \]

2 is a zero of the polynomial function \[ f(x)=x^4+kx^3+22x^2-6x-20. \] If \(-2,\alpha,\beta\) are the roots of the equation \[ x^3+3x^2+2kx-40=0 \] and \(\alpha<\beta\), then \(2\alpha+3\beta=\)

The equation formed with the roots obtained by diminishing the roots of the equation \( x^{4}+3x^{3}-7x^{2}+4x+1=0 \) by 'h', does not contain the \( x^{2} \) term. If the possible values of such 'h' are \( h_{1}<0 \) and \( h_{2}>0, \) then which one of the following is true?

If one root of the cubic equation \[ x^3+36=7x^2 \] is double of another, then the number of negative roots is

The sum of the real roots of the equation \[ x^4-2x^3+x-380=0 \] is