Learn all Concepts of Chapter 4 Class 10 (with VIDEOS). Check - Quadratic Equations - Class 10
Last updated at July 16, 2019 by Teachoo
Transcript
Ex 4.1 ,1 Check whether the following are quadratic equations : (i) (๐ฅ+1)^2 = 2(x โ 3) (๐ฅ+1)^2 = 2(x โ 3) ๐ฅ2+12+2ร๐ฅร1=2(๐ฅโ3) ๐ฅ2 + 1 + 2๐ฅ = 2๐ฅ โ 6 ๐ฅ2 + 1+ 2๐ฅ โ 2๐ฅ + 6 = 0 ๐ฅ2 + 1 +6 = 0 ๐ฅ2 + 7 = 0 ๐ฅ2 + 0๐ฅ + 7 = 0 Since , it is of the form ๐๐ฅ2 + ๐๐ฅ + ๐ =0 Where ๐ = 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 (โ2)x x2 โ 2x = โ6 + 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) (๐ฅ โ 2)(๐ฅ + 1)= (๐ฅ โ 1)(๐ฅ + 3) ๐ฅ (๐ฅ + 1) โ 2 (๐ฅ + 1) = ๐ฅ (๐ฅ + 3) โ 1 (๐ฅ + 3) ๐ฅ2 + ๐ฅ โ 2๐ฅ โ 2 = ๐ฅ2 + 3๐ฅ โ ๐ฅ โ 3 ๐ฅ2 + ๐ฅ โ 2๐ฅ โ 2 โ ๐ฅ2 โ 3๐ฅ + ๐ฅ + 3 = 0 (๐ฅ2 โ ๐ฅ2 ) + (๐ฅ โ 2๐ฅ โ 3๐ฅ + ๐ฅ ) โ 2 + 3 = 0 0 โ 3๐ฅ + 1 = 0 โ 3๐ฅ + 1 = 0 Since , highest power is 1 not 2, It is not in the form of ๐๐ฅ2 + ๐๐ฅ + 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) (๐ฅ โ 3) (2๐ฅ + 1) = ๐ฅ (๐ฅ + 5) ๐ฅ (2๐ฅ + 1) โ 3(2๐ฅ + 1) = ๐ฅ (๐ฅ + 5) 2๐ฅ2 + ๐ฅ โ 6๐ฅ โ3 = ๐ฅ2 + 5๐ฅ 2๐ฅ2 + ๐ฅ โ 6๐ฅ โ 3 โ ๐ฅ2 โ 5๐ฅ = 0 2๐ฅ2 โ ๐ฅ2 +๐ฅ โ 6๐ฅ โ 5๐ฅ โ 3 = 0 ๐ฅ2 โ 10 ๐ฅ โ 3 = 0 Since, the equation is of the form ๐๐ฅ2 + ๐๐ฅ + 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) (2๐ฅ โ 1)(๐ฅ โ 3)= (๐ฅ + 5)(๐ฅ โ 1) 2๐ฅ (๐ฅ โ 3) โ 1 (๐ฅ โ 3) = ๐ฅ (๐ฅ โ 1) + 5 (๐ฅ โ 1) 2๐ฅ2 โ 6๐ฅ โ ๐ฅ + 3 = ๐ฅ2 โ ๐ฅ + 5๐ฅ โ 5 2๐ฅ2 โ 6๐ฅ โ ๐ฅ + 3 โ ๐ฅ2 + ๐ฅ โ 5๐ฅ + 5 = 0 2๐ฅ2 โ ๐ฅ2 โ 6๐ฅ โ ๐ฅ + ๐ฅ โ 5๐ฅ + 3 + 5 = 0 ๐ฅ2 โ 11๐ฅ + 8 = 0 Since it is of the form ๐๐ฅ2 + ๐๐ฅ + 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 ๐ฅ2 + 3๐ฅ + 1 = (๐ฅ โ 2)^2 ๐ฅ2 + 3๐ฅ +1 = ๐ฅ2+22โ2 ร๐ฅร2 ๐ฅ2 +3๐ฅ +1 = ๐ฅ2 + 4 โ 4๐ฅ ๐ฅ2 + 3๐ฅ + 1 โ ๐ฅ2 โ 4+ 4๐ฅ= 0 ๐ฅ2 โ ๐ฅ2 + 3๐ฅ + 4๐ฅ + 1 โ 4 = 0 0 + 7๐ฅ โ 3 = 0 7๐ฅ โ 3 = 0 Since , highest power is 1 not 2, It is not in the form of ๐๐ฅ2 + ๐๐ฅ + 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 ร๐ฅร2(๐ฅ+2)=2๐ฅ (x2 โ 1) ๐ฅ3 +8+6๐ฅ(๐ฅ+2)=2๐ฅ3โ2๐ฅ ๐ฅ2 + 8 + 6๐ฅ2 + 12๐ฅ = 2๐ฅ3 โ 2๐ฅ ๐ฅ3 + 8 + 6๐ฅ2 + 12๐ฅ โ 2๐ฅ3 + 2๐ฅ = 0 ๐ฅ3 โ 2๐ฅ3 + 6๐ฅ2 + 12๐ฅ + 2๐ฅ + 8 = 0 โ ๐ฅ3 + 6๐ฅ2 +14๐ฅ + 8 = 0 Since highest power is 3 and not 2, It is not in the form of ๐๐ฅ2 + ๐๐ฅ + 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 ๐ฅ3 โ 4๐ฅ2 โ ๐ฅ+ 1 = (๐ฅ โ 2)^3 ๐ฅ3 โ 4๐ฅ2 โ ๐ฅ+1 = ๐ฅ3 โ23 โ3ร๐ฅร2(xโ2) ๐ฅ3 โ 4๐ฅ2 โ ๐ฅ+1 = ๐ฅ3 โ 8 โ 6๐ฅ (๐ฅ โ 2) ๐ฅ3 โ 4๐ฅ2 โ ๐ฅ +1 = ๐ฅ3 โ 8 โ 6๐ฅ2 + 12 ๐ฅ ๐ฅ3 โ 4๐ฅ2 โ ๐ฅ + 1 โ ๐ฅ3 + 8 + 6๐ฅ2 โ 12๐ฅ = 0 ๐ฅ3 โ ๐ฅ3 โ 4๐ฅ2 + 6๐ฅ2 โ ๐ฅ โ 12๐ฅ + 1 + 8 = 0 0 + 2๐ฅ2 โ 13๐ฅ + 9 = 0 2๐ฅ2 โ 13๐ฅ + 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
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