Page 1 1. 2 2 7 x x 6 0 Sol: (i) 2 Here, a 2, 7, 2 7 x x 6 0 b c 6 Discriminant D is diven by: 2 2 7 4 2 6 D b 4 a c 49 48 1 (ii) 2 3 2 x x 8 0 Here, Page 2 1. 2 2 7 x x 6 0 Sol: (i) 2 Here, a 2, 7, 2 7 x x 6 0 b c 6 Discriminant D is diven by: 2 2 7 4 2 6 D b 4 a c 49 48 1 (ii) 2 3 2 x x 8 0 Here, 3, 2, 8 a b c Discriminant D is given by: 2 2 4 2 4 3 8 4 96 92 D b a c (iii) 2 2 5 2 4 0 x x Here, 2, 5 2, 4 a b c Discriminant D is given by: 2 2 4 5 2 4 2 4 25 2 32 50 32 18 D b a c (iv) 2 3 2 2 2 3 0 x x Here, 3 2 2, 2 3 a b c Discriminant D is given by: 2 2 4 2 2 4 3 2 3 4 2 8 3 8 24 32 D b a c (v) 1 2 1 0 x x 2 2 3 1 0 x x Comparing it with 2 0, a x b x c we get Page 3 1. 2 2 7 x x 6 0 Sol: (i) 2 Here, a 2, 7, 2 7 x x 6 0 b c 6 Discriminant D is diven by: 2 2 7 4 2 6 D b 4 a c 49 48 1 (ii) 2 3 2 x x 8 0 Here, 3, 2, 8 a b c Discriminant D is given by: 2 2 4 2 4 3 8 4 96 92 D b a c (iii) 2 2 5 2 4 0 x x Here, 2, 5 2, 4 a b c Discriminant D is given by: 2 2 4 5 2 4 2 4 25 2 32 50 32 18 D b a c (iv) 2 3 2 2 2 3 0 x x Here, 3 2 2, 2 3 a b c Discriminant D is given by: 2 2 4 2 2 4 3 2 3 4 2 8 3 8 24 32 D b a c (v) 1 2 1 0 x x 2 2 3 1 0 x x Comparing it with 2 0, a x b x c we get 2, 3 1 a b a n d c Discriminant, 2 2 4 3 4 2 1 9 8 1 D b a c (vi) 2 1 2 x x 2 2 1 0 x x Here, 2, 1, 1 a b c Discriminant D is given by: 2 2 4 1 4 2 1 1 8 9 D b ac Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 2. 2 4 1 0 x x Sol: Given: 2 4 1 0 x x On comparing it with 2 0, a x b x c we get: 1, 4 1 a b a n d c Discriminant D is given by: 2 4 D b a c 2 4 4 1 1 16 4 20 20 0 Hence, the roots of the equation are real. Roots and are given by: 2 2 5 4 20 4 2 5 2 5 2 2 1 2 2 2 2 5 4 20 4 2 5 2 5 2 2 2 2 b D a b D a Page 4 1. 2 2 7 x x 6 0 Sol: (i) 2 Here, a 2, 7, 2 7 x x 6 0 b c 6 Discriminant D is diven by: 2 2 7 4 2 6 D b 4 a c 49 48 1 (ii) 2 3 2 x x 8 0 Here, 3, 2, 8 a b c Discriminant D is given by: 2 2 4 2 4 3 8 4 96 92 D b a c (iii) 2 2 5 2 4 0 x x Here, 2, 5 2, 4 a b c Discriminant D is given by: 2 2 4 5 2 4 2 4 25 2 32 50 32 18 D b a c (iv) 2 3 2 2 2 3 0 x x Here, 3 2 2, 2 3 a b c Discriminant D is given by: 2 2 4 2 2 4 3 2 3 4 2 8 3 8 24 32 D b a c (v) 1 2 1 0 x x 2 2 3 1 0 x x Comparing it with 2 0, a x b x c we get 2, 3 1 a b a n d c Discriminant, 2 2 4 3 4 2 1 9 8 1 D b a c (vi) 2 1 2 x x 2 2 1 0 x x Here, 2, 1, 1 a b c Discriminant D is given by: 2 2 4 1 4 2 1 1 8 9 D b ac Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 2. 2 4 1 0 x x Sol: Given: 2 4 1 0 x x On comparing it with 2 0, a x b x c we get: 1, 4 1 a b a n d c Discriminant D is given by: 2 4 D b a c 2 4 4 1 1 16 4 20 20 0 Hence, the roots of the equation are real. Roots and are given by: 2 2 5 4 20 4 2 5 2 5 2 2 1 2 2 2 2 5 4 20 4 2 5 2 5 2 2 2 2 b D a b D a Thus, the roots of the equation are 2 5 and 2 5 . 3. 2 6 4 0 x x Sol: Given: 2 6 4 0 x x On comparing it with 2 0, a x b x c we get: 1, 6 4 a b a n d c Discriminant D is given by: 2 4 D b a c 2 6 4 1 4 36 16 20 0 Hence, the roots of the equation are real. Roots and are given by: 2 3 3 6 20 6 2 5 3 5 2 2 1 2 2 2 3 5 6 20 6 2 5 3 5 2 2 2 2 b D a b D a Thus, the roots of the equation are 3 2 5 and 3 2 5 . 4. 2 2 4 0. x x Sol: The given equation is 2 2 4 0. x x Comparing it with 2 0, a x b x c we get 2, 1 a b and 4 c Discriminant, 2 2 4 1 4 2 4 1 32 33 0 D b a c So, the given equation has real roots. Now, 33 D 1 33 1 33 2 2 2 4 1 33 1 33 2 2 2 4 b D a b D a Page 5 1. 2 2 7 x x 6 0 Sol: (i) 2 Here, a 2, 7, 2 7 x x 6 0 b c 6 Discriminant D is diven by: 2 2 7 4 2 6 D b 4 a c 49 48 1 (ii) 2 3 2 x x 8 0 Here, 3, 2, 8 a b c Discriminant D is given by: 2 2 4 2 4 3 8 4 96 92 D b a c (iii) 2 2 5 2 4 0 x x Here, 2, 5 2, 4 a b c Discriminant D is given by: 2 2 4 5 2 4 2 4 25 2 32 50 32 18 D b a c (iv) 2 3 2 2 2 3 0 x x Here, 3 2 2, 2 3 a b c Discriminant D is given by: 2 2 4 2 2 4 3 2 3 4 2 8 3 8 24 32 D b a c (v) 1 2 1 0 x x 2 2 3 1 0 x x Comparing it with 2 0, a x b x c we get 2, 3 1 a b a n d c Discriminant, 2 2 4 3 4 2 1 9 8 1 D b a c (vi) 2 1 2 x x 2 2 1 0 x x Here, 2, 1, 1 a b c Discriminant D is given by: 2 2 4 1 4 2 1 1 8 9 D b ac Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 2. 2 4 1 0 x x Sol: Given: 2 4 1 0 x x On comparing it with 2 0, a x b x c we get: 1, 4 1 a b a n d c Discriminant D is given by: 2 4 D b a c 2 4 4 1 1 16 4 20 20 0 Hence, the roots of the equation are real. Roots and are given by: 2 2 5 4 20 4 2 5 2 5 2 2 1 2 2 2 2 5 4 20 4 2 5 2 5 2 2 2 2 b D a b D a Thus, the roots of the equation are 2 5 and 2 5 . 3. 2 6 4 0 x x Sol: Given: 2 6 4 0 x x On comparing it with 2 0, a x b x c we get: 1, 6 4 a b a n d c Discriminant D is given by: 2 4 D b a c 2 6 4 1 4 36 16 20 0 Hence, the roots of the equation are real. Roots and are given by: 2 3 3 6 20 6 2 5 3 5 2 2 1 2 2 2 3 5 6 20 6 2 5 3 5 2 2 2 2 b D a b D a Thus, the roots of the equation are 3 2 5 and 3 2 5 . 4. 2 2 4 0. x x Sol: The given equation is 2 2 4 0. x x Comparing it with 2 0, a x b x c we get 2, 1 a b and 4 c Discriminant, 2 2 4 1 4 2 4 1 32 33 0 D b a c So, the given equation has real roots. Now, 33 D 1 33 1 33 2 2 2 4 1 33 1 33 2 2 2 4 b D a b D a Hence, 1 33 4 and 1 33 4 are the roots of the given equation. 5. 2 25 30 7 0 x x Sol: Given: 2 25 30 7 0 x x On comparing it with 2 0, a x b x x we get; 25, 30 7 a b a n d c Discriminant D is given by: 2 2 4 30 4 25 7 D b a c 900 700 200 200 0 Hence, the roots of the equation are real. Roots and are given by: 10 3 2 3 2 30 200 30 10 2 2 2 25 50 50 5 10 3 2 3 2 30 200 30 10 2 2 2 25 50 50 5 b D a b D a Thus, the roots of the equation are 3 2 3 2 . 5 5 a n d 6. 2 16 24 1 x x Sol: Given: 2 2 16 24 1 16 24 1 0 x x x x On comparing it with 2 0, a x b x x we get; 16, 24 1 a b a n d c Discriminant D is given by: 2 4 D b a c 2 24 4 16 1Read More

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