The roots of quadratic equation x² - 1 = 0 are :

1. 0

2. 1

3. -1

4. ±1

Which of the following equation represents a line equally inclined to the axes ?

1. 2x - 3y + 7 = 0

2. x - y = 7

3. x = 7

4. y = -7

While factorizing a given polynomial, using remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x³ + 7x² + 2x - 3.

(a) Is the student's solution correct stating that (2x + 1) is a factor of the given polynomial ? Given a valid reason for your answer.

(b) Factorize the given polynomial completely.

A line segment joining P (2, -3) and Q (0, -1) is cut by the x-axis at the point R. A line AB cuts the y-axis at T(0, 6) and is perpendicular to PQ at S. Find the :

(a) equation of line PQ

(b) equation of line AB

(c) coordinates of points R and S.