List of top Mathematics Questions on Polynomials asked in AP EAPCET

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax - b = 0 \), and \( \alpha^2 + \beta^2 \) and \( \alpha^3 + \beta^3 \) are the roots of \( Ax^2 + Bx + C = 0 \), then \( C = \ldots \)
The minimum value of \( f(x) = \frac{x^2 - 2x + 3}{x^2 - 4x + 7} \) is:
If the sum of the cubes of the roots of the equation \( x^3 - ax^2 + bx - c = 0 \) is zero, then \( a^3 + 3c = \):
If \( x^2 + x - 6 \) is a factor of \( 2x^3 + x^2 + ax + b \), then \( 6a + 13b = \) ?
If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:
If \( P(x) = 0 \) is a polynomial of least degree with integer coefficients and \( \sqrt{2} + \sqrt{3}i \) is one of its roots, then that equation is:
If \( \alpha_1, \alpha_2, \alpha_3 \) are the roots of the equation \( x^3 + 3x + 2 = 0 \), then \( \alpha_1^5 + \alpha_2^5 + \alpha_3^5 \) is:
If $ 3 + i $ and $ 2 - \sqrt{3} $ are the roots of the equation $ f(x) = a_0 + a_1 x + a_2 x^2 + ... + a_n x^n $, where $ a_0, a_1, ..., a_n \in \mathbb{Z} $, then the least value of $ n $ and the value of $ a_0 $ are respectively:
If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + 3x^2 + 4x + 5 = 0 $, then the cubic equation whose roots are $ 1 + 4\alpha, 1 + 4\beta, 1 + 4\gamma $ is:
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
The sum of the real roots of the equation: $$ x^4 - 2x^3 + x - 380 = 0 $$ is:
If one root of the cubic equation: $$ x^3 + 36 = 7x^2 $$ is double of another, then the number of negative roots is: