Polynomials Mock Tests

Let the roots of x³ − 3x² + 3x − 7 = 0 be alpha, beta, gamma. Then alpha³ + beta³ + gamma³ equals

If 2 and 3 are the zeros of the polynomial x² − 5x + k, what is the value of k?

One of the factors of the polynomial x² + 7x + 12 is:

Which of the following is a polynomial in x?

Let P(x) be a polynomial of degree 4 such that P(0) = 1, P(1) = 3, P(-1) = 1, P(2) = 31, and P(-2) = 3. Then P(x) is:

If f(x) = x² − 5x + 6, then f(2) is

The factorisation of x² + 7x + 12 is:

If α and β are the zeros of the polynomial p(x) = 2x² - 5x + k, and they satisfy α + β = αβ, find the value of k.