Question

If α and β are the zeroes of the polynomial p(x) = x² − ax − b, then the value of (α + β + αβ) is equal to :

Find the value(s) of 'k' so that the quadratic equation 4x² + kx + 1 = 0 has real and equal roots.

If 'α' and 'β', are the zeroes of the polynomial p(y) = y² − 5y + 3, then find the value of α⁴β³ + α³β⁴.

If – 4 is a zero of the polynomial p(x) = x² – x – (2 + 2k), then the value of k is :