Quadratic Equations Solutions

Complete Notes of class 10th math chapter 1 solutions in 10th Class Mathematics Urdu Medium by Dear Respectable Sir M. Ramzan Suib. These computerized notes are very helpful in the preparation of class 10th math chapter 1 solutions for students of the 10th class Mathematics and these are according to the paper patterns of all Punjab boards.

• Important 10th class math solution chapter 1 pdf for all students of Punjab  Textbook Board.
• Define quadratic equation.
• Define reciprocal equation.
• Define exponential equation.
• Important class 10 maths chapter 1 solutions exercise 1.1 for all students of Punjab  Textbook Board.
• Define radical equation.
• (i) The standard form of the quadratic equation is ..........
• (ii) The number of methods to solve a quadratic equation are .......
• Important class 10 maths chapter 1 solutions exercise 1.2 for all students of Punjab  Textbook Board.
• (iii) The name of the method to derive a quadratic formula is .......
• (iv) The solution of the equation ax^2 + bx + c = 0, a ≠ 0 is .......
• (v) The solution set of 25x^2 - 1 = 0 is .......
• Important class 10 maths chapter 1 solutions exercise 1.3 for all students of Punjab  Textbook Board.
• (vi) An equation of the form 2^2x - 3.2^x + 5 = 0 is called a/an ....... equation.
• (vii) The solution set of the equation x^2 - 9 = 0 is .......
• (viii) An equation of the type x^4 + x^3 + x^2 + x + 1 = 0 called a/an ....... equation.
• Important class 10 maths chapter 1 solutions exercise 1.4 for all students of Punjab  Textbook Board.
• (ix) A root of an equation, which do not satisfy the equation is called ....... root.
• (x) An equation involving impression of the variable under ....... is called radical  equation.
• Important 10 class math chapter 1 solution for all students of Punjab  Textbook Board.
• An equation which contains the square of the unknown (variable) quantity, but no higher power, is called a quadratic equation or an equation of the second degree.
• An equation is said to be a reciprocal equation, if it remains unchanged, when x is replaced by 1 / x.
• Important 10 class math exercise 1.1 solution for all students of Punjab  Textbook Board.
• In exponential equations, variables occur in exponents.
• An equation involving expression under the radical sign is called a radical equation.
• Quadratic formula for ax² + bx + c = 0, a ≠ 0 is:  x = -b ± √b² - 4ac / 2a
• Important 10 class math exercise 1.1 solution pdf for all students of Punjab  Textbook Board.
• Any quadratic equation is solved by the following three methods. (i) Factorization , (ii) Completing square , (iii) Quadratic formula
• Example: Solve 5x² = 30x by factorization.
• Important 10 class math exercise 1.2 solution pdf for all students of Punjab  Textbook Board.
• Solution: 5x² = 30x
• 5x² - 30x = 0 which is factorized as; 5x ( x - 6 ) = 0 Either 5x = 0 or x - 6 = 0 ,  x = 0 or x = 6 , so x = 0, x = 6 are the roots of the given equation. Thus, the solution set is { 0, 6 }.
• Important 10 class math exercise 1.2 solutions for all students of Punjab  Textbook Board.
• Remember that: Cancelling of x on both sides of 5x² = 30x means the loss of one root i.e., x = 0
• Use of quadratic formula: The quadratic formula is a useful tool for solving all those equations which can or can not be factorized. 
• Important 10 class math exercise 1.3 solution for all students of Punjab  Textbook Board.
• The method to solve the quadratic equation by using quadratic formula is illustrated through the following examples.
• Example: Solve the quadratic equation 2 + 9x = 5x² by using quadratic formula.
• Important 10 class math exercise 1.4 solution for all students of Punjab  Textbook Board.
• Solution: 2 + 9x = 5x²   The given equation in standard form can be written as: 5x² - 9x - 2 = 0 
• Comparing with the standard quadratic equation ax² + bx + c = 0, we observe that  a = 5 , b = - 9 , c = - 2  Putting the values of a, b and e in quadratic formula:  x = -b ± √b² - 4ac / 2a , we have  x = -(-9) ± √(-9)² - 4(5)(-2) / 2(5)
• Important 10 class math exercise 1.3 solution pdf for all students of Punjab  Textbook Board.
• x = 9 ± √81 + 40 / 10 = 9 ± √121 / 10  = 9 ± 11 / 10 
• Either x = 9 +11 / 10  or  x = 9 -11 /10
• Important 10 class math exercise 1.4 solution pdf for all students of Punjab  Textbook Board.
•  x = 20 / 10 = 2   ,  x = -2 / 10 = - 1 / 5
• 2, -1 / 5 are the roots of given equation.
• Thus, the solution set is { - 1 / 5, 2 }
• Important 10 class math exercise 1.3 solution pdf download for all students of Punjab  Textbook Board.