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Quadratic Equations

Directions (Qs. 1 - 25): In the following questions, two equations are given. You have to solve both and establish the relation between given variables.

1. I. x2 - 9x + 20 = 0       II. y2 - 7y + 12 = 0
1) x > y           2) x y             3) x < y           4) x y       
5) x = y or the relationship cannot be established
Sol: x2 - 9x + 20 = 0
⇒ x2 - 5x - 4x + 20 = 0
⇒ x (x - 5) - 4 (x - 5) = 0
⇒ (x - 5) (x - 4) = 0
⇒ x = 5 or 4 y2 - 7y + 12 = 0
⇒ y2 - 4y - 3y + 12 = 0
⇒ y (y - 4) - 3 (y - 4) = 0
⇒ (y - 4) (y - 3) = 0
⇒ y = 4 or 3
∴ x y  
Ans: 2 

 

2. I. x3 = 64        II. 2y2 - 17y + 36 = 0
1) x > y         2) x y            3) x < y             4) x y
5) x = y or the relationship cannot be established (SBI JA - 2020)
Sol: x3 = 64
⇒ x = 3√64 = 4
2y2 - 17y + 36 = 0
⇒ 2y2 - 8y - 9y + 36 = 0
⇒ 2y (y - 4) - 9 (y - 4) = 0
⇒ y = 4 or 4.5
∴ x y  
Ans: 4

 

3. I. x2 - x - 56 = 0       II. y2 - 20y + 99 = 0
1) x > y          2) x y              3) x < y              4) x y
5) x = y or the relationship cannot be established
Sol: x2 - x - 56 = 0
By solving, x = -7 and 8
y2 - 20y + 99 = 0
By solving, y = 9 and 11
∴ x < y
Ans: 3

 

4. I. 2x2 + 19x + 42 = 0        II. 4y2 + 43y + 30 = 0
1) x > y            2) x y              3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2018)
Sol: 2x2 + 19x + 42 = 0
By solving, x values are -6 & -3.5
4y2 + 43y + 30 = 0
By solving, y values are -10 & -0.75
∴ Relation can’t be established
Ans: 5

 

5. I. 2x2 + 48 = 20x          II. y2 - 6 = y
1) x > y          2) x y             3) x < y              4) x y
5) x = y or the relationship cannot be established
Sol: 2x2 + 48 = 20x
By solving, x values are 6 & 4
y2 - 6 = y
By solving, y values are 3 & -2
∴ x > y  
Ans: 1

 

6. I. 2x2 - x - 6 = 0       II. 6y2 + 17y + 5 = 0
1) x > y          2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2020)
Sol: 2x2 - x - 6 = 0
By solving, x values are 2 & -1.5
6y2 + 17y + 5 = 0
By solving, y values are -2.5 & -0.33
∴ Relation can’t be established
Ans: 5


7. I. x2 - 6x + 8 = 0       II. y2 + y - 6 = 0
1) x > y          2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 6x + 8 = 0
by solving we get x values as 2 and 4
y2 + y - 6 = 0
by solving we get y values as 2 and -3
∴ x y
Ans: 2

 

8. I. x2 + 17x + 66 = 0          II. y2 + 10y + 24 = 0
1) x > y          2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 17x + 66 = 0
By solving, x = -6 and -11 y2 + 10y + 24 = 0
By solving, y = -4 and -6
∴ x y
Ans: 4

 

9. I. x2 + x - 20 = 0       II. y2 - 4y - 21 = 0
1) x > y        2) x y        3) x < y          4) x y
5) x = y or the relationship cannot be established
Sol: x2 + x - 20 = 0
By solving, x values are 4 & -5 y2 - 4y - 21 = 0
By solving, y values are 7 & -3
∴ Relation can’t be established
Ans: 5
Shortcut: When in both equations, if constant values are negative (in this question, -20 & -21) then the answer is always no relation.

 

10. I. 5x2 + 3x - 2 = 0      II. 4y2 - 7y + 3 = 0
1) x > y          2) x y              3) x < y                  4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2020)
Sol: 5x2 + 3x - 2 = 0
By solving, x values are 0.4 & -1
4y2 - 7y + 3 = 0
By solving, y values are 1 & 0.75
∴ x < y
Ans: 3

 

11. I. x2 + 10x + 9 = 0       II. 2y2 + 14y + 24 = 0
1) x > y           2) x y              3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 10x + 9 = 0
by solving we get x values as - 9 and -1
2y2 + 14y + 24 = 0
by solving we get y values as -3 and -4
∴ Relation can’t be established
Ans: 5

 

12. I. x2 - 16x + 63 = 0      II. y2 - 18y + 81 = 0
1) x > y            2) x y              3) x < y            4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 16x + 63 = 0
By solving x values are 7 & 9
y2 - 18y + 81 = 0
By solving y values are 9 & 9
∴ x y  
Ans: 4

 

13. I. x2 - 11x + 28 = 0      II. y2 - 12y + 36 = 0
1) x > y           2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2018)
Sol: x2 - 11x + 28 = 0
By solving, x values are 7 & 4
y2 - 12y + 36 = 0
By solving, y values are 6 & 6
∴ Relation can’t be established
Ans: 5

 

14. I. 6x2 + 31x + 33 = 0      II. y2 - 32y + 247 = 0
1) x > y        2) x y           3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2016)
Sol: 6x2 + 31x + 33 = 0 
By solving, x values are -3 2/3 & -1 1/2
y2 - 32y + 247 = 0
By solving, y values are 13 & 19
∴ x < y  
Ans: 3

 

15. I. x2 + 7x + 10 = 0         II. y2 + y = 2
1) x > y            2) x y             3) x < y              4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 7x + 10 = 0
by solving we get x values as -2 and -5
y2 + y = 2
by solving we get y values as 1 and -2
∴ x y
Ans: 4

 

16. I. x2 - 8x + 15 = 0         II. y2 - 12y + 36 = 0
1) x > y         2) x y          3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 8x + 15 = 0
By solving x = 3 & 5
y2 - 12y + 36 = 0
By solving y = 6 & 6
∴ x < y
Ans: 3

 

17. I. 2x2 + 13x + 21 = 0          II. 2y2 + 27y + 88 = 0
1) x > y          2) x y             3) x < y                  4) x y
5) x = y or the relationship cannot be established
Sol: 2x2 + 13x + 21 = 0
x values are -3 & -3.5
2y2 + 27y + 88 = 0
y values are -8 & -5.5
∴ x > y
Ans: 1

 

18. I. x2 - 13x + 40 = 0          II. y2 - 6y + 5 = 0
1) x > y             2) x y            3) x < y           4) x y   
5) x = y or the relationship cannot be established (SBI JA - 2020)
Sol: x2 - 13x + 40 = 0
By solving, x values are 8 & 5
y2 - 6y + 5 = 0
By solving, y values are 5 & 1
∴ x y
\Ans: 2

 

19. I. x2 - 11x + 28 = 0   II. y2 - 9y + 18 = 0
1) x > y          2) x y           3) x < y           4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 11x + 28 = 0
By solving, x = 7 and 4
y2 - 9y + 18 = 0
By solving, y = 6 and 3
∴ Relation can’t be established
Ans: 5

 

20. I. x2 + 36 = 12x           II. 11y - 42 = 4y
1) x > y          2) x y            3) x < y            4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 36 = 12x
by solving we get x values as 6 and 6
11y - 42 = 4y
by solving we get y values as 6
∴ x = y
Ans: 5

 

21. I. x2 - 15x + 44 = 0        II. y2 - 23y + 132 = 0
1) x > y        2) x y         3) x < y          4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 15x + 44 = 0
By solving, x values are 11 & 4
y2 - 23y + 132 = 0
By solving, y values are 11 & 12
∴ x y  
Ans: 4

 

22. I. x2 - 4 = 0        II. y2 - 6y + 9 = 0
1) x > y         2) x y           3) x < y             4) x y
5) x = y or the relationship cannot be established (SBI JA - 2020)
Sol: x2 - 4 = 0
⇒ x = √4 = ± 2
x values are +2 & -2
y2 - 6y + 9 = 0
y values are 3 & 3
∴ x < y
Ans: 3

 

23. I. 2x2 - 17x + 33 = 0    II. y2 - 8y + 15 = 0
1) x > y          2) x y           3) x < y         4) x y
5) x = y or the relationship cannot be established
Sol: 2x2 - 17x + 33 = 0
x values are 3 & 5.5
y2 - 8y + 15 = 0
y values are 3 & 5
∴ x y
Ans: 2

 

24. I. x2 + 11x + 30 = 0       II. y2 - 23y + 76 = 0
1) x > y          2) x y          3) x < y          4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 11x + 30 = 0
By solving, x values are -5 & -6
y2 - 23y + 76 = 0
By solving, y values are 19 & 4
∴ x < y
Ans: 3

 

25. I. 3x2 - 14x + 16 = 0      II. 5y2 - 16y + 12 = 0
1) x > y           2) x y        3) x < y       4) x y
5) x = y or the relationship cannot be established (SBI JA - 2018)
Sol: 3x2 - 14x + 16 = 0 
By solving, x values are 2 & 2. 2/3 
5y2 - 16y + 12 = 0
By solving, y values are 2 & 1. 1/5
∴ x y
Ans: 2

Posted Date : 24-05-2021

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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