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QUADRATIC EQUATIONS

Directions (Qs. 1 - 25): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and giveb answer.
 

A) if x > y    B) if x < y
C) if x > y    D) if x < y
E) if x = y or relationship between x and y cannot be established

 

1. I. x2 + 5x + 6 = 0
II. y2 + 4y + 4 = 0
Sol: x2 + 5x + 6 = 0; x1 = −3; x2 = −2
y2 + 4y + 4 = 0; y1 = −2; y2 = −2
Comparison of x and y values
−3 < −2; −3 < −2; −2 = −2; −2 = −2
Hence, x £ y is correct.

 

2. I. x2 − 25x + 156 = 0
II. y2 + 13y + 42 = 0
Sol: x2 − 25x + 156 = 0; x1 = 13; x2 = 12
y2 + 13y + 42 = 0; y1 = −7; y2 = −6
Comparison of x and y values
13 > −7; 13 > −7; 12 > −6; 12 > −6
Hence, x > y is correct.

 

3. I. x2 + 9x + 14 = 0
II. y2 + 12y − 45 = 0
Sol: x2 + 9x + 14 = 0; x1 = −7; x2 = −2
y2 + 12y − 45 = 0; y1 = −15; y2 = 3
Comparison of x and y values
−7 > −15; −7 > −15; −2 < 3; −2 < 3
Hence, the relationship between x and y cannot be established.

 

4. I. x2 − 26x + 168 = 0
II. y2 + 48y + 575 = 0
Sol: x2 − 26x + 168 = 0; x1 = 12; x2 = 14
y2 + 48y + 575 = 0; y1 = −23; y2 = −25
Comparison of x and y values
12 > −23; 12 > −25; 14 > −23; 14 > −25
Hence, x > y is correct.

 

5. I. x2 + 44x + 483 = 0
II. y2 + 30y + 224 = 0
Sol: x2 + 44x + 483 = 0; x1 = −21; x2 = −23
y2 + 30y + 224 = 0; y1 = −16; y2 = −14
Comparison of x and y values
−21 < −16; −21 < −14
−23 < −16; −23 < −14
Hence, x < y is correct.

 

6. I. x2 + 23x + 130 = 0
II. y2 + 35y + 306 = 0
Sol: x2 + 23x + 130 = 0; x1 = −13; x2 = −10
y2 + 35y + 306 = 0; y1 = −18; y2 = −17
Comparison of x and y values
−13 > −18; −13 > −17
−10 > −18; −10 > −17
Hence, x > y is correct.

 

7. I. x2 + 44x + 483 = 0
II. y2 + 30y + 224 = 0
Sol: x2 + 44x + 483 = 0; x1 = −21; x2 = −23
y2 + 30y + 224 = 0; y1 = −16; y2 = −14
Comparison of x and y values
−21 < −16; −21 < −14
−23 < −16; −23 < −14
Hence, x < y is correct.

 

8. I. x2 + 18x + 77 = 0
II. 3y2 − 14y + 15 = 0
Sol: x2 + 18x + 77 = 0; x1 = −11; x2 = −7
3y2 − 14y + 15 = 0; y1 = 3;
Comparison of x and y values


Hence, x < y is correct.

 

9. I. 17x2 − 14x − 3 = 0
II. 2y2 − 7y − 60 = 0
Sol: 17x2 − 14x − 3 = 0 ; x1 = ; x2 = 1

2y2 − 7y − 60 = 0: y1 = -4 :

Comparison of x and y values


Hence, the relationship between x and y cannot be established.

 

10. I. x2 − x − 12 = 0
II. y2 − 17y − 84 = 0
Sol: x2 − x − 12 = 0; x1 = 4; x2 = −3
y2 − 17y − 84 = 0; y1 = 9; y2 = −13
Comparison of x and y values
4 < 9; 4 > −13; −3 < 9; −3 > −13
Hence, the relationship between x and y cannot be established.

 

11. I. x2 = 144
II. 7y2 − 19y + 10 = 0
Sol: x2 = 144; x1 = 12; x2 = −12
7y2 − 19y + 10 = 0 ; y1 = 2 ;

Comparison of x and y values


Hence, the relationship between x and y cannot be established.

 

12. I. x2 + 2x − 35 = 0
II. 2y2 − 7y − 60 = 0
Sol: x2 + 2x − 35 = 0; x1 = −7; x2 = 5
2y2 − 7y − 60 = 0; y1 = −4;  
Comparison of x and y values

Hence, the relationship between x and y cannot be established.

 

13. I. 4x2 − 8x − 5 = 0
II. 6y2 + 5y + 1 = 0
Sol: 4x2 − 8x − 5 = 0 ;
6y2 + 5y + 1 = 0 ;
Comparison of x and y values


Hence, x > y is correct.

 

14. I. x2 = 92
II. y2 + 8y + 15 = 0
Sol: x2 = 92 ; x1 = 9 ; x2 = 9
y2 + 8y + 15 = 0 ; y1 = −3 ; y2 = −5
Comparison of x and y values
9 > −3 ; 9 > −5 ; 9 > −3 ; 9 > −5
Hence, x > y is correct.

 

15. I. 2x2 − 3x − 20 = 0
II. y2 + 14y − 32 = 0
Sol: 2x2 − 3x − 20 = 0 ; x1 = 4 ; x2 =
y2 + 14y − 32 = 0 ; y1 = −16 ; y2 = 2
Comparison of x and y values

Hence, the relationship between x and y cannot be established.

 

16. I. x2 + 13x + 42 = 0
II. y2 + 31y + 238 = 0
Sol: x2 + 13x + 42 = 0 ; x1 = −6 ; x2 = −7
y2 + 31y + 238 = 0 ;
y1 = −18 ; y2 = −19
Comparison of x and y values
−6 > −18 ; −6 > −19
−7 > −18 ; −7 > −19
Hence, x > y is correct.

 

17. I. x2 + 215 = 1176
II. y2 + 41y + 418 = 0
Sol: x2 + 215 = 1176 ; x1 = 31 ; x2 = −31
y2 + 41y + 418 = 0 ; y1 = −19; y2 = −22
Comparison of x and y values
31 > −19; 31 > −22
−31 < −19; −31 < −22
Hence, the relationship between x and y cannot be established.

 

18. I. x2 + 37x + 342 = 0
II. y2 = 256
Sol: x2 + 37x + 342 = 0; x1 = −18 ; x2 = −19
y2 = 256 ; y1 = −16 ; y2 = 16
Comparison of x and y values
−18 < −16 ; −18 < 16
−19 < −16 ; −19 < −16
Hence, x < y is correct.

 

19. I. x2 − 21x + 108 = 0
II. 5y2 + 23y + 24 = 0
Sol: x2 − 21x + 108 = 0 ; x1 = 9 ; x2 = 12
5y2 + 23y + 24 = 0 ; y1 = −3 ; y2 =
Comparison of x and y values

Hence, the relationship between x and y cannot be established.
Hence, x > y is correct.

 

20. I. x3 + 340 = 2537
II. y2 + 44y + 483 = 0
Sol: x3 + 340 = 2537; x1 = 13 ; x2 = 13
y2 + 44y + 483 = 0; y1 = −21 ; y2 = −23
Comparison of x and y values
13 > −21; 13 > −23
13 > −21; 13 > −23
Hence, x > y is correct.

 

21. I. x2 = 4
II. y2 + 4y + 4 = 0
Sol: x2 = 4; x1 = −2; x2 = 2
y2 + 4y + 4 = 0; y1 = −2; y2 = −2
Comparison of x and y values
−2 = −2 ; −2 = −2 ; 2 > −2 ; 2 > −2
Hence, x > y is correct.

 

22. I. 3x2 − 14x + 15 = 0
II. 2y2 − 7y − 60 = 0
Sol: 3x2 − 14x + 15 = 0 ; x1 = 3 ;
2y2 − 7y − 60 = 0 ; y1 = −4 ;
Comparison of x and y values

Hence, the relationship between x and y cannot be established.

 

23. I. x2 + 29x + 208 = 0
II. y2 + 31y + 238 = 0
Sol: x2 + 29x + 208 = 0; x1 = −16 ; x2 = −13
y2 + 31y + 238 = 0; y1 = −18 ; y2 = −19
Comparison of x and y values
−16 > −18 ; −16 > −19
−13 > −18 ; −13 > −19
Hence, x > y is correct

 

24. I. x2 − 11x + 30 = 0
II. y2 + 14y − 32 = 0
Sol: x2 − 11x + 30 = 0; x1 = 5 ; x2 = 6
y2 + 14y − 32 = 0; y1 = −16 ; y2 = 2
Comparison of x and y values
5 > −16 ; 5 > 2 ; 6 > −16 ; 6 > 2
Hence, x > y is correct.

 

25. 
Sol:
x1 = 16 ; x2 = 16
y2 = 256; y1 = −16; y2 = 16
Comparison of x and y values
16 > −16; 16 = 16
16 > −16; 16 = 16
Hence, x > y is correct.

 

Key 

1-D   2-A   3-E   4-A   5-B   6-A   7-B   8-B   9-E   10-E   11-E   12-E   13-C   14-A   15-E   16-A   17-E   18-B   19-A   20-A   21-C   22-E   23-A  24-A   25-C

Posted Date : 23-07-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్లో వచ్చే ప్రకటనలు అనేక దేశాల నుండి, వ్యాపారస్తులు లేదా వ్యక్తుల నుండి వివిధ పద్ధతులలో సేకరించబడతాయి. ఆయా ప్రకటనకర్తల ఉత్పత్తులు లేదా సేవల గురించి ఈనాడు యాజమాన్యానికీ, ఉద్యోగస్తులకూ ఎటువంటి అవగాహనా ఉండదు. కొన్ని ప్రకటనలు పాఠకుల అభిరుచిననుసరించి కృత్రిమ మేధస్సు సాంకేతికతతో పంపబడతాయి. ఏ ప్రకటనని అయినా పాఠకులు తగినంత జాగ్రత్త వహించి, ఉత్పత్తులు లేదా సేవల గురించి తగిన విచారణ చేసి, తగిన జాగ్రత్తలు తీసుకొని కొనుగోలు చేయాలి. ఉత్పత్తులు / సేవలపై ఈనాడు యాజమాన్యానికి ఎటువంటి నియంత్రణ ఉండదు. కనుక ఉత్పత్తులు లేదా సేవల నాణ్యత లేదా లోపాల విషయంలో ఈనాడు యాజమాన్యం ఎటువంటి బాధ్యత వహించదు. ఈ విషయంలో ఎటువంటి ఉత్తర ప్రత్యుత్తరాలకీ తావు లేదు. ఫిర్యాదులు తీసుకోబడవు.

 

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