The below questions require to be understood thoroughly!

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 = 0 which 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.Givenlog_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) = 0 are 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.