Ex 4.1, 1 - Check whether following are quadratic equations - Ex 4.1

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
Ask Download

Transcript

Ex 4.1 ,1 Check whether the following are quadratic equations : (i) (๐‘ฅ+1)^2 = 2(x โ€“ 3) (๐‘ฅ+1)^2 = 2(x โ€“ 3) ๐‘ฅ2+12+2ร—๐‘ฅร—1=2(๐‘ฅโˆ’3) ๐‘ฅ2 + 1 + 2๐‘ฅ = 2๐‘ฅ โ€“ 6 ๐‘ฅ2 + 1+ 2๐‘ฅ โ€“ 2๐‘ฅ + 6 = 0 ๐‘ฅ2 + 1 +6 = 0 ๐‘ฅ2 + 7 = 0 ๐‘ฅ2 + 0๐‘ฅ + 7 = 0 Since , it is of the form ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ =0 Where ๐‘Ž = 1, ๐‘ = 0, ๐‘ = 7 Hence, it is a quadratic equation Ex 4.1 ,1 Check whether the following are quadratic equations : (ii) x2 โ€“ 2x = (-2) (3 โ€“ x) x2 โ€“ 2x = (-2) (3 โ€“ x) x2 โ€“ 2x = (-2)3 โ€“ (โ€“2)x x2 โ€“ 2x = โ€“6 + 2x x2 โ€“ 2x โ€“ 2x + 6 = 0 x2 โ€“ 4x + 6 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = โ€“ 4 , c = 6 Hence, it is a quadratic equation . Ex 4.1 ,1 Check whether the following are quadratic equations : (iii) (x โ€“ 2)(x + 1) = (x โ€“ 1)(x + 3) (๐‘ฅ โ€“ 2)(๐‘ฅ + 1)= (๐‘ฅ โ€“ 1)(๐‘ฅ + 3) ๐‘ฅ (๐‘ฅ + 1) โ€“ 2 (๐‘ฅ + 1) = ๐‘ฅ (๐‘ฅ + 3) โ€“ 1 (๐‘ฅ + 3) ๐‘ฅ2 + ๐‘ฅ โ€“ 2๐‘ฅ โ€“ 2 = ๐‘ฅ2 + 3๐‘ฅ โ€“ ๐‘ฅ โ€“ 3 ๐‘ฅ2 + ๐‘ฅ โ€“ 2๐‘ฅ โ€“ 2 โ€“ ๐‘ฅ2 โ€“ 3๐‘ฅ + ๐‘ฅ + 3 = 0 (๐‘ฅ2 โ€“ ๐‘ฅ2 ) + (๐‘ฅ โ€“ 2๐‘ฅ โ€“ 3๐‘ฅ + ๐‘ฅ ) โ€“ 2 + 3 = 0 0 โ€“ 3๐‘ฅ + 1 = 0 โ€“ 3๐‘ฅ + 1 = 0 Since , highest power is 1 not 2, It is not in the form of ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ =0 Hence, it is not a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (iv) (x โ€“ 3)(2x +1) = x(x + 5) (๐‘ฅ โ€“ 3) (2๐‘ฅ + 1) = ๐‘ฅ (๐‘ฅ + 5) ๐‘ฅ (2๐‘ฅ + 1) โ€“ 3(2๐‘ฅ + 1) = ๐‘ฅ (๐‘ฅ + 5) 2๐‘ฅ2 + ๐‘ฅ โ€“ 6๐‘ฅ โˆ’3 = ๐‘ฅ2 + 5๐‘ฅ 2๐‘ฅ2 + ๐‘ฅ โ€“ 6๐‘ฅ โ€“ 3 โ€“ ๐‘ฅ2 โ€“ 5๐‘ฅ = 0 2๐‘ฅ2 โ€“ ๐‘ฅ2 +๐‘ฅ โ€“ 6๐‘ฅ โ€“ 5๐‘ฅ โ€“ 3 = 0 ๐‘ฅ2 โ€“ 10 ๐‘ฅ โ€“ 3 = 0 Since, the equation is of the form ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ = 0 Where, a = 1, b = โ€“ 10, c = โ€“ 3 Hence it is a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (v) (2x โ€“ 1)(x โ€“ 3) = (x + 5)(x โ€“ 1) (2๐‘ฅ โ€“ 1)(๐‘ฅ โ€“ 3)= (๐‘ฅ + 5)(๐‘ฅ โ€“ 1) 2๐‘ฅ (๐‘ฅ โ€“ 3) โ€“ 1 (๐‘ฅ โ€“ 3) = ๐‘ฅ (๐‘ฅ โ€“ 1) + 5 (๐‘ฅ โ€“ 1) 2๐‘ฅ2 โ€“ 6๐‘ฅ โ€“ ๐‘ฅ + 3 = ๐‘ฅ2 โ€“ ๐‘ฅ + 5๐‘ฅ โ€“ 5 2๐‘ฅ2 โ€“ 6๐‘ฅ โ€“ ๐‘ฅ + 3 โ€“ ๐‘ฅ2 + ๐‘ฅ โ€“ 5๐‘ฅ + 5 = 0 2๐‘ฅ2 โ€“ ๐‘ฅ2 โ€“ 6๐‘ฅ โ€“ ๐‘ฅ + ๐‘ฅ โ€“ 5๐‘ฅ + 3 + 5 = 0 ๐‘ฅ2 โ€“ 11๐‘ฅ + 8 = 0 Since it is of the form ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ =0 Where a = 1, b = โ€“ 11, c = 8 Hence it is a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (vi) x2 + 3x + 1 = (x โ€“ 2)2 ๐‘ฅ2 + 3๐‘ฅ + 1 = (๐‘ฅ โ€“ 2)^2 ๐‘ฅ2 + 3๐‘ฅ +1 = ๐‘ฅ2+22โˆ’2 ร—๐‘ฅร—2 ๐‘ฅ2 +3๐‘ฅ +1 = ๐‘ฅ2 + 4 โ€“ 4๐‘ฅ ๐‘ฅ2 + 3๐‘ฅ + 1 โ€“ ๐‘ฅ2 โ€“ 4+ 4๐‘ฅ= 0 ๐‘ฅ2 โ€“ ๐‘ฅ2 + 3๐‘ฅ + 4๐‘ฅ + 1 โ€“ 4 = 0 0 + 7๐‘ฅ โ€“ 3 = 0 7๐‘ฅ โ€“ 3 = 0 Since , highest power is 1 not 2, It is not in the form of ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ =0 Hence, it is not a quadratic equation. Ex 4.1 ,1 Check whether the following are quadratic equations : (vii) (x + 2)3 = 2x (x2 โ€“ 1) (x + 2)3 = 2x (x2 โ€“ 1) x3 + 23 + 3 ร—๐‘ฅร—2(๐‘ฅ+2)=2๐‘ฅ (x2 โ€“ 1) ๐‘ฅ3 +8+6๐‘ฅ(๐‘ฅ+2)=2๐‘ฅ3โˆ’2๐‘ฅ ๐‘ฅ2 + 8 + 6๐‘ฅ2 + 12๐‘ฅ = 2๐‘ฅ3 โ€“ 2๐‘ฅ ๐‘ฅ3 + 8 + 6๐‘ฅ2 + 12๐‘ฅ โ€“ 2๐‘ฅ3 + 2๐‘ฅ = 0 ๐‘ฅ3 โ€“ 2๐‘ฅ3 + 6๐‘ฅ2 + 12๐‘ฅ + 2๐‘ฅ + 8 = 0 โ€“ ๐‘ฅ3 + 6๐‘ฅ2 +14๐‘ฅ + 8 = 0 Since highest power is 3 and not 2, It is not in the form of ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ =0 Hence, it is not a quadratic equation Ex 4.1 ,1 Check whether the following are quadratic equations : (viii) x3 โ€“ 4x2 โ€“ x + 1 = (x โ€“ 2)3 ๐‘ฅ3 โ€“ 4๐‘ฅ2 โ€“ ๐‘ฅ+ 1 = (๐‘ฅ โ€“ 2)^3 ๐‘ฅ3 โ€“ 4๐‘ฅ2 โ€“ ๐‘ฅ+1 = ๐‘ฅ3 โ€“23 โˆ’3ร—๐‘ฅร—2(xโˆ’2) ๐‘ฅ3 โ€“ 4๐‘ฅ2 โ€“ ๐‘ฅ+1 = ๐‘ฅ3 โ€“ 8 โ€“ 6๐‘ฅ (๐‘ฅ โ€“ 2) ๐‘ฅ3 โ€“ 4๐‘ฅ2 โ€“ ๐‘ฅ +1 = ๐‘ฅ3 โ€“ 8 โ€“ 6๐‘ฅ2 + 12 ๐‘ฅ ๐‘ฅ3 โ€“ 4๐‘ฅ2 โ€“ ๐‘ฅ + 1 โ€“ ๐‘ฅ3 + 8 + 6๐‘ฅ2 โ€“ 12๐‘ฅ = 0 ๐‘ฅ3 โ€“ ๐‘ฅ3 โ€“ 4๐‘ฅ2 + 6๐‘ฅ2 โ€“ ๐‘ฅ โ€“ 12๐‘ฅ + 1 + 8 = 0 0 + 2๐‘ฅ2 โ€“ 13๐‘ฅ + 9 = 0 2๐‘ฅ2 โ€“ 13๐‘ฅ + 9 = 0 It is of the form ax2 + bx + c = 0 Where a = 2, b = โ€“ 13 and c = 9 Hence, it is a quadratic equation

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.