10 Class Math Chapter 2 Solution

Important full 10 class math chapter 2 solution in Mathematics Urdu Medium by Dear Respectable Sir M. Ramzan Suib. These computerized notes are very helpful in the preparation of 10 class math chapter 2 solution for students of Mathematics and these are according to the paper patterns of all Punjab boards.

• Important 10 class math exercise 2.1 solution for all students of Punjab  Textbook Board.
• Nature of the roots of a quadratic equation:
• On solving quadratic equations, we get different kinds of roots. Now we will discuss the nature or characteristics of the roots of the quadratic equation without actually solving it. 
• Important 10 class math exercise 2.1 solution pdf for all students of Punjab  Textbook Board.
• Discriminant ( b² - 4ac ) of the quadratic expression ax² + bx + c.
• We know that two roots of the equation ax² + bx + c = 0, a ≠ 0  are x = -b + √b² - 4ac / 2a  and x = -b - √b² - 4ac / 2a.
• Important 10 class math exercise 2.2 solution pdf for all students of Punjab  Textbook Board.
• The nature of these roots depends on the value of the expression "( b² - 4ac )" which is called the "discriminant" of the quadratic equation (i) or the quadratic expression ax² + bx + c.
• Important 10 class math exercise 2.3 solution for all students of Punjab  Textbook Board.
• To find the discriminant of a given quadratic equation.:
• We explain the procedure to find the discriminant of a given quadratic equation through the following example: 
• Important 10 class math exercise 2.4 solution for all students of Punjab  Textbook Board.
• Example: Find the discriminant of the following equations.
• (a) 2x² - 7x + 1 = 0 , Solution:  2x² - 7x + 1 = 0 , Here a = 2 ,  b= - 7 , c = 1 , Disc, = b² - 4ac = (-7)² - 4 (2) (1) = = 49 - 8 = 41
• Important 10 class math exercise 2.5 solution for all students of Punjab  Textbook Board.
• (b) x² - 3x + 3 = 0 , Solution: Here a = 1 , b = - 3 , c = 3 , Disc. = Disc, = b² - 4ac = ( - 3)² - 4 (1) (3) = 9 - 12 =  -3
• Nature of the roots of a quadratic equation through discriminant:
• Important 10 class math exercise 2.6 solution for all students of Punjab  Textbook Board.
• The roots of the quadratic equation ax² + bx + c = 0, ( a ≠ 0 ) are x = - b ± √b² - 4ac / 2a and its discriminant is ( b² - 4ac ).
• When a, b and c are rational numbers.
• Important 10 class math exercise 2.7 solution for all students of Punjab  Textbook Board.
• (1) If b² - 4ac > 0 and is a perfect square, then the roots are rational (real) and unequal.
• (ii) If b² - 4ac > 0 and is not a perfect square, then the roots are irrational (real) and unequal.
• Important 10 class math exercise 2.8 solution for all students of Punjab  Textbook Board.
• (iii) If b² - 4ac = 0, then the roots are rational (real) and equal.
• (iv) If b² - 4ac < 0, then the roots are imaginary (complex conjugates).
• Important class 10 maths chapter 2 solutions exercise 2.2 for all students of Punjab  Textbook Board.
• Determine the nature of the roots of a given quadratic equation and verify the result by solving the equation:
• We illustrate the procedure through the following examples:
• Example: Using discriminant, find the nature of the roots of the following equations and verify the results by solving the equations.
• Important class 10 maths chapter 2 solutions exercise 2.3 for all students of Punjab  Textbook Board.
• (a) x² - 5x + 5 = 0 , (b) 2x² - x + 1 = 0 , (c) x² + 8x + 16 = 0 ,  (d) 7x² + 8x + 1 = 0