If alpha, beta are roots of x^2 - 3x + 1 = 0, then alpha^3 + beta^3 equals:

The equations x^2 + 2x + 3 = 0 and ax^2 + bx + c = 0 (a,b,c real) have a common root. Then a:b:c equals:

The set of values of k for which x^2 + kx + 1 > 0 for all x in R is:

If one root of x^2 + px + 12 = 0 is 4, the value of p and the other root are:

Both roots of x^2 - 2ax + a^2 - 1 = 0 lie between -2 and 4. The range of a is: