For what values of m, is mx² + mx + 8x + 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 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)?

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

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

For what value of k does the system of equations x - ky = 2 and 3x + 2y = -5 NOT have a unique solution?