5 Important Quadratic Equations Questions for IBPS PO

equations

In each of these questions’ two equations are given. You have to solve these equations and give answer

Ques 1. 

I. x² − 6x = 7
II. 2y² + 13y + 15 = 0 

a. if x < y
b. if x > y
c. if x = y or relation cannot be established
d. if x ≥ y
e. if x ≤ y

Ques 2. 

I. 3x² − 7x + 2 = 0 II. 2y² − 11x + 15 = 0 
a. if x < y
b. if x > y
c. if x = y or relation cannot be established
d. if x ≥ y
e. if x ≤ y

Ques 3. 

I. 10X² − 7x + 1 = 0 II. 35y² − 12y + 1 = 0 
a. if x < y
b. if x > y
c. if x = y or relation cannot be established
d. if x ≥ y
e. if x ≤ y

Ques 4.

I. 4x² = 25 II. 2y² − 13y + 21 = 0 
a. if x < y
b. if x > y
c. if x = y or relation cannot be established
d. if x ≥ y
e. if x ≤ y

Ques 5.

I. 3x² + 7x = 6 II. 6(2y² + 1) = 17y 
a. if x < y
b. if x > y
c. if x = y or relation cannot be established
d. if x ≥ y
e. if x ≤ y

ANSWERS:

1. b
2. a
3. d
4. a
5. c

Explanation and solution:

1. x² − 6x = 7
x(x-7)+(x-7)=0
→ x=7,-1
2y² + 13y + 15 = 0
2y(y+5)+3(y+5)=0
→y=-5, -3/2
If x=7,y=-5
x > y
x > y
→if =-1
x > y
x > y
i.e x > y

2. 3x² − 7x + 2 = 0
3x(x-2)+(x-2)=0
→x=2,-1/3
2y² − 11x + 15 = 0
2y(y-3)-5(y-3)=0
→y=3,5/2
If x=2
x<y,x<y
if x=-1/3
x<y,x<y
i.e x<y

3. 10X² − 7x + 1 = 0
5x (2x-1)-(2x-1)=0
→x=1/2, 1/5
35y² − 12y + 1 = 0
7y (5y-1)-(5y-1)=0
→y=1/7,1/5
If x=1/5
x>y
x=y
If x=1/2
x>y
x>y
i.e x ≥ y

4. 4x² = 25
→X=5/2, -5/2
2y² − 13y + 21 = 0
2y(y-3)-7(y-3)=0
→y=3,7/2
If x=5/2
x<y
x<y
if x=-5/2
Both cases x<y
i.e x<y

5. 3x² + 7x = 6
3x(x+3)-2(x+3)=0
→x= 2/3,-3
10y² – 7y + 1 = 0
5y(2y-1)-(2y-1)=0
→y=1/2, 1/5
If x=2/3
x>y
x>y
if x=-3
x<y
x<y
i.e relation cannot be established

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