For how many integral values of k, the equation x² - 4x + k = 0, where k is an integer has real roots and both of them lie in the interval (0, 5) ? 

How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?

α and β are distinct real roots of the quadratic equation x² + ax + b = 0. Which of the following statements is/are sufficient to find α ? 

1. α + β = 0, α² + β² = 2

2. αβ² = -1, a = 0

Select the correct answer using the code given below :

Consider the following for the next two (02) items that follow :

A quadratic equation is given by

(3 + 2√2)x² - (4 + 2√3)x + (8 + 4√3) = 0

What is the HM of the roots of the equation ?