Hello tutors! Please help me with solving these very difficult questions.

1.Determine the parameter of 'a' given such an equation which has both real & distinct roots, (a + 1)x2 + 2(a+1)x + (a - 2) = 0.

2.Given equations x2 + 3x + 3 = 0 and x2 + bx + c = 0which have one root in common, determine the product ofb * c .

3.Determine where the real roots of ax2 - x + a = 0 arex1, x2, the set of all the values of parameter 'a' where|x1 - x1| < 1.

4.Determine the value of f(x) where f(x) = Ax2 + Bx + C = 0 and 2A, A + B, C are integers.

5.Given an equation x2 + 5|x| + 6 = 0, determine the sum of real root.

6.Determine in the equation |x - 2| + x(x - 4) + 2 = 0 the no. of solutions.

7.Find the biggest integer that would satisfy (x2 - 1)/(x - 2)(x - 3).

8.Given log x2 (x + 1) > 0, determine a set which is complete of values x and that would satisfy the equation.

9.The roots of an equation 3x2 + 2x + p(p - 1) = 0are of opposite sign, determine the set of values of p.

10.An inequality (2x2 - 2x - 3) / (x2 + x + 1) a satisfying all real x results to a real number, let's say 'a' being called a good number. Determine the set of all real numbers.