For what values of m, is mx² + mx + x8 + 9 a perfect square?

If 2 is a zero of the polynomial p(x) = x³ + 3x² - 6x - a then what is the sum of the squares of the other zeros of the polynomial ?

If x + 1/x = k and x² + 1/x² = k, then values of k are

If a, b, c, d, e and f satisfy 2a = 3b = 6c = 9d = 12e = 18f, then what is the value of (a + b)/(c + d + e + f)?

For what value of k, the system of equations x-ky = 2 and 3x+2y = -5 has a unique solution?

Suppose n is an integer such that the sum of the digits of n is 2, and 10¹⁰ <n < 10¹¹, The number of different values for n is