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Page 1 1. 2 6 x x 3 0 Sol: 2 2 6 3 0 6 x x x x 2 3 2 2 2 x x 3 3 3 3 (Adding 2 3 on both sides) 2 x 3 3 9 6 3 6 x (Taking square root on the both sides) Page 2 1. 2 6 x x 3 0 Sol: 2 2 6 3 0 6 x x x x 2 3 2 2 2 x x 3 3 3 3 (Adding 2 3 on both sides) 2 x 3 3 9 6 3 6 x (Taking square root on the both sides) 3 6 3 6 3 6 3 6 x o r x x o r x Hence, 3 6 and 3 6 are the roots of the given equation. 2. 2 4 1 0 x x Sol: 2 2 4 1 0 4 1 x x x x 2 2 2 2 2 2 1 2 x x (Adding 2 2 on both sides) 2 2 1 4 3 x 2 3 x (Taking square root on the both sides) 2 3 2 3 2 3 2 3 x o r x x o r x Hence, 2 3 and 2 3 are the roots of the given equation. 3. 2 8 2 0 x x Sol: 2 2 8 2 0 8 2 x x x x 2 2 2 2 4 4 2 4 x x (Adding 2 4 on both sides) 2 4 2 16 18 x 4 18 3 2 x (Taking square root on the both sides) 4 3 2 4 3 2 4 3 2 4 3 2 x or x x or x Hence, 4 3 2 and 4 3 2 are the roots of the given equation. 4. 2 4 4 3 3 0 x x Sol: 2 2 4 4 3 3 0 4 4 3 3 x x x x 2 2 2 2 2 2 3 3 3 3 x x [Adding 2 3 on both sides] Page 3 1. 2 6 x x 3 0 Sol: 2 2 6 3 0 6 x x x x 2 3 2 2 2 x x 3 3 3 3 (Adding 2 3 on both sides) 2 x 3 3 9 6 3 6 x (Taking square root on the both sides) 3 6 3 6 3 6 3 6 x o r x x o r x Hence, 3 6 and 3 6 are the roots of the given equation. 2. 2 4 1 0 x x Sol: 2 2 4 1 0 4 1 x x x x 2 2 2 2 2 2 1 2 x x (Adding 2 2 on both sides) 2 2 1 4 3 x 2 3 x (Taking square root on the both sides) 2 3 2 3 2 3 2 3 x o r x x o r x Hence, 2 3 and 2 3 are the roots of the given equation. 3. 2 8 2 0 x x Sol: 2 2 8 2 0 8 2 x x x x 2 2 2 2 4 4 2 4 x x (Adding 2 4 on both sides) 2 4 2 16 18 x 4 18 3 2 x (Taking square root on the both sides) 4 3 2 4 3 2 4 3 2 4 3 2 x or x x or x Hence, 4 3 2 and 4 3 2 are the roots of the given equation. 4. 2 4 4 3 3 0 x x Sol: 2 2 4 4 3 3 0 4 4 3 3 x x x x 2 2 2 2 2 2 3 3 3 3 x x [Adding 2 3 on both sides] 2 2 3 3 3 0 2 3 0 3 2 x x x Hence, 3 2 is the repeated root of the given equation. 5. 2 2 5 3 0 x x Sol: 2 2 5 3 0 x x 2 4 10 6 0 x x (Multiplying both sides by 2) 2 4 10 6 x x 2 2 2 5 5 5 2 2 2 6 2 2 2 x x [Adding 2 5 2 on both sides] 2 2 5 25 24 25 49 7 2 6 2 4 4 4 2 x 5 7 2 2 2 x (Taking square root on both sides) 5 7 5 7 2 2 2 2 2 2 x o r x 7 5 2 2 1 2 2 3 x or 7 5 12 2 6 2 2 2 x 1 2 x or 3 x Hence, 1 2 and 3 are the roots of the given equation. 6. 2 3 2 0 x x Sol: 2 3 2 0 x x 2 9 3 6 0 x x (Multiplying both sides by 3) 2 9 3 6 x x 2 2 2 1 1 1 3 2 3 6 2 2 2 x x [Adding 2 1 2 on both sides] Page 4 1. 2 6 x x 3 0 Sol: 2 2 6 3 0 6 x x x x 2 3 2 2 2 x x 3 3 3 3 (Adding 2 3 on both sides) 2 x 3 3 9 6 3 6 x (Taking square root on the both sides) 3 6 3 6 3 6 3 6 x o r x x o r x Hence, 3 6 and 3 6 are the roots of the given equation. 2. 2 4 1 0 x x Sol: 2 2 4 1 0 4 1 x x x x 2 2 2 2 2 2 1 2 x x (Adding 2 2 on both sides) 2 2 1 4 3 x 2 3 x (Taking square root on the both sides) 2 3 2 3 2 3 2 3 x o r x x o r x Hence, 2 3 and 2 3 are the roots of the given equation. 3. 2 8 2 0 x x Sol: 2 2 8 2 0 8 2 x x x x 2 2 2 2 4 4 2 4 x x (Adding 2 4 on both sides) 2 4 2 16 18 x 4 18 3 2 x (Taking square root on the both sides) 4 3 2 4 3 2 4 3 2 4 3 2 x or x x or x Hence, 4 3 2 and 4 3 2 are the roots of the given equation. 4. 2 4 4 3 3 0 x x Sol: 2 2 4 4 3 3 0 4 4 3 3 x x x x 2 2 2 2 2 2 3 3 3 3 x x [Adding 2 3 on both sides] 2 2 3 3 3 0 2 3 0 3 2 x x x Hence, 3 2 is the repeated root of the given equation. 5. 2 2 5 3 0 x x Sol: 2 2 5 3 0 x x 2 4 10 6 0 x x (Multiplying both sides by 2) 2 4 10 6 x x 2 2 2 5 5 5 2 2 2 6 2 2 2 x x [Adding 2 5 2 on both sides] 2 2 5 25 24 25 49 7 2 6 2 4 4 4 2 x 5 7 2 2 2 x (Taking square root on both sides) 5 7 5 7 2 2 2 2 2 2 x o r x 7 5 2 2 1 2 2 3 x or 7 5 12 2 6 2 2 2 x 1 2 x or 3 x Hence, 1 2 and 3 are the roots of the given equation. 6. 2 3 2 0 x x Sol: 2 3 2 0 x x 2 9 3 6 0 x x (Multiplying both sides by 3) 2 9 3 6 x x 2 2 2 1 1 1 3 2 3 6 2 2 2 x x [Adding 2 1 2 on both sides] 2 2 1 1 25 5 3 6 2 4 4 2 x 1 5 3 2 2 x (Taking square root on both sides) 1 5 1 5 3 3 2 2 2 2 x or x 5 1 6 3 3 2 2 2 x or 5 1 4 3 2 2 2 2 x 2 1 3 x o r x Hence, 1 and 2 3 are the roots of the given equation. 7. 2 8 14 15 0 x x Sol: 2 8 14 15 0 x x 2 16 28 30 0 x x (Multiplying both sides by 2) 2 16 28 30 x x 2 2 2 7 7 7 4 2 4 30 2 2 2 x x [Adding 2 7 2 on both sides] 2 2 7 49 169 13 4 30 2 4 4 2 x 7 13 4 2 2 x (Taking square root on both sides) 7 13 7 13 4 4 2 2 2 2 x o r x 13 7 20 4 10 2 2 2 x or 13 7 6 4 3 2 2 2 x 5 3 2 4 x or x Hence, 5 2 and 3 4 are the roots of the given equation. 8. 2 7 3 4 0 x x Sol: 2 7 3 4 0 x x 2 49 21 28 0 x x (Multiplying both sides by 7) Page 5 1. 2 6 x x 3 0 Sol: 2 2 6 3 0 6 x x x x 2 3 2 2 2 x x 3 3 3 3 (Adding 2 3 on both sides) 2 x 3 3 9 6 3 6 x (Taking square root on the both sides) 3 6 3 6 3 6 3 6 x o r x x o r x Hence, 3 6 and 3 6 are the roots of the given equation. 2. 2 4 1 0 x x Sol: 2 2 4 1 0 4 1 x x x x 2 2 2 2 2 2 1 2 x x (Adding 2 2 on both sides) 2 2 1 4 3 x 2 3 x (Taking square root on the both sides) 2 3 2 3 2 3 2 3 x o r x x o r x Hence, 2 3 and 2 3 are the roots of the given equation. 3. 2 8 2 0 x x Sol: 2 2 8 2 0 8 2 x x x x 2 2 2 2 4 4 2 4 x x (Adding 2 4 on both sides) 2 4 2 16 18 x 4 18 3 2 x (Taking square root on the both sides) 4 3 2 4 3 2 4 3 2 4 3 2 x or x x or x Hence, 4 3 2 and 4 3 2 are the roots of the given equation. 4. 2 4 4 3 3 0 x x Sol: 2 2 4 4 3 3 0 4 4 3 3 x x x x 2 2 2 2 2 2 3 3 3 3 x x [Adding 2 3 on both sides] 2 2 3 3 3 0 2 3 0 3 2 x x x Hence, 3 2 is the repeated root of the given equation. 5. 2 2 5 3 0 x x Sol: 2 2 5 3 0 x x 2 4 10 6 0 x x (Multiplying both sides by 2) 2 4 10 6 x x 2 2 2 5 5 5 2 2 2 6 2 2 2 x x [Adding 2 5 2 on both sides] 2 2 5 25 24 25 49 7 2 6 2 4 4 4 2 x 5 7 2 2 2 x (Taking square root on both sides) 5 7 5 7 2 2 2 2 2 2 x o r x 7 5 2 2 1 2 2 3 x or 7 5 12 2 6 2 2 2 x 1 2 x or 3 x Hence, 1 2 and 3 are the roots of the given equation. 6. 2 3 2 0 x x Sol: 2 3 2 0 x x 2 9 3 6 0 x x (Multiplying both sides by 3) 2 9 3 6 x x 2 2 2 1 1 1 3 2 3 6 2 2 2 x x [Adding 2 1 2 on both sides] 2 2 1 1 25 5 3 6 2 4 4 2 x 1 5 3 2 2 x (Taking square root on both sides) 1 5 1 5 3 3 2 2 2 2 x or x 5 1 6 3 3 2 2 2 x or 5 1 4 3 2 2 2 2 x 2 1 3 x o r x Hence, 1 and 2 3 are the roots of the given equation. 7. 2 8 14 15 0 x x Sol: 2 8 14 15 0 x x 2 16 28 30 0 x x (Multiplying both sides by 2) 2 16 28 30 x x 2 2 2 7 7 7 4 2 4 30 2 2 2 x x [Adding 2 7 2 on both sides] 2 2 7 49 169 13 4 30 2 4 4 2 x 7 13 4 2 2 x (Taking square root on both sides) 7 13 7 13 4 4 2 2 2 2 x o r x 13 7 20 4 10 2 2 2 x or 13 7 6 4 3 2 2 2 x 5 3 2 4 x or x Hence, 5 2 and 3 4 are the roots of the given equation. 8. 2 7 3 4 0 x x Sol: 2 7 3 4 0 x x 2 49 21 28 0 x x (Multiplying both sides by 7) 2 49 21 28 x x 2 2 2 3 3 3 7 2 7 28 2 2 2 x x [Adding 2 3 2 on both sides] 2 2 3 9 121 11 7 28 2 4 4 2 x 3 11 7 2 2 x (Taking square root on both sides) 3 11 3 11 7 7 2 2 2 2 x or x 11 3 8 7 4 2 2 2 x or 11 3 14 7 7 2 2 2 x 4 1 7 x o r x Hence, 4 7 and 1 are the roots of the given equation. 9. 2 3 2 1 0 x x Sol: 2 3 2 1 0 x x 2 9 6 3 0 x x (Multiplying both sides by 3) 2 9 6 3 x x 2 2 2 3 2 3 1 1 3 1 x x [Adding 2 1 on both sides] 2 2 3 1 3 1 4 2 x 3 1 2 x (Taking square root on both sides) 3 1 2 x or 3 1 2 x 3 3 x or 3 1 x 1 x or 1 3 x Hence, 1 and 1 3 are the roots of the given equation. 10. 2 5 6 2 0 x x Sol: 2 5 6 2 0 x x 2 25 30 10 0 x x (Multiplying both sides by 5) 2 25 30 10 x xRead More
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1. What are quadratic equations? 
2. How do you solve quadratic equations? 
3. What is the discriminant of a quadratic equation? 
4. Can quadratic equations have irrational or imaginary roots? 
5. Are there any reallife applications of quadratic equations? 
120 videos463 docs105 tests


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