Quadratic Equation Quiz Set -2 IBPS PO | IBPS RRB| IBPS Clerk| SBI| RBI

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Quadratic Equation Quiz

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In the following questions, two equations are given. You have to solve both the equations and choose the correct option :

1. I. 9x2+17x+8=0

    II. y2+8y+7=0

A. x ≤ y

B. x ≥ y

C. x < y

D. x > y

E. x = y or no specific relation can be established

Show Correct Answers

B. x ≥ y

First equation –
9x²+17x+8=0
=>9x²+9x+8x+8=0
=>9x(x+1)+8(x+1)=0
=>(9x+8)(x+1)=0
Thus we get, x = -8/9 or -1
Second equation –
y²+8y+7=0
=>y²+y+7y+7=0
=>y(y+1)+7(y+1)=0
=>(y+7)(y+1)=0
Thus we get, y = -7 or -1
Hence x ≥ y

 

2. I. x²-10x+24 = 0

   II. 3y²+4y-15 = 0

A. x ≤ y

B. x ≥ y

C. x < y

D. x > y

E. x = y or no specific relation can be established

Show Correct Answers

D. x > y

First equation –
x²-10x+24=0
=>x²-4x-6x+24=0
=>x(x-4)-6(x-4)=0
=>(x-6)(x-4)=0
Thus we get, x = 6 or 4
Second equation –
3y²+4y-15=0
=>3y²+9y-5y-15=0
=>3y(y+3)-5(y+3)=0
=>(3y-5)(y+3)=0
Thus we get, y = 5/3 or -3
Hence x > y

3. I. x²+x-20 = 0

   II.9y²-55y+6 = 0

A. x ≤ y

B. x ≥ y

C. x < y

D. x > y

E. x = y or no specific relation can be established

Show Correct Answers

E. x = y or no specific relation can be established

First equation –
x²+x-20=0
=>x²+5x-4x-20=0
=>x(x+5)-4(x+5)=0
=>(x-4)(x+5)=0
Thus we get, x = 4 or -5
Second equation –
9y²-55y+6=0
=>9y²-54y-y+6=0
=>9y(y-6)-1(y-6)=0
=>(9y-1)(y-6)=0
Thus we get, y = 1/9 or 6
One value of x lies between the two values of y and vice versa, hence the relation cannot be determined.

4. I. x²-2x-24 = 0

   II.y²+4y-45 = 0

A. x ≤ y

B. x ≥ y

C. x < y

D. x > y

E. x = y or no specific relation can be established

Show Correct Answers

E. x = y or no specific relation can be established

First equation –
x²-2x-24=0
=>x²-6x+4x-24=0
=>x(x-6)+4(x-6)=0
=>(x+4)(x-6)=0
Thus we get, x = -4 or 6
Second equation –
y²+4y-45=0
=>y²-5y+9y-45=0
=>y(y-5)+9(y-5)=0
=>(y+9)(y-5)=0
Thus we get, y = -9 or 5
One value of x lies between the two values of y and vice versa, hence the relation cannot be determined

5. I. x²+9x+8 = 0

   II. 3y²+19y-14 = 0

A. x ≤ y

B. x ≥ y

C. x < y

D. x > y

E. x = y or no specific relation can be established

Show Correct Answers

E. x = y or no specific relation can be established

First equation –
x²+9x+8=0
=>x²+8x+x+8=0
=>x(x+8)+1(x+8)=0
=>(x+1)(x+8)=0
Thus we get, x = -1 or -8
Second equation –
3y²+19y-14=0
=>3y²+21y-2y-14=0
=>3y(y+7)-2(y+7)=0
=>(3y-2)(y+7)=0
Thus we get, y = 2/3 or -7
One value of x lies between the two values of y and vice versa, hence the relation cannot be determined

6.Based on the equations given choose the option which is true :
I. 10x2-31x-14 =0
II. 5y2-8y-4 = 0

A. If x ≤ y

B. If x ≥ y

C. If x < y

D. If x > y

E. If x = y or no specific relation can be established

Show Correct Answers

E. If x = y or no specific relation can be established

First equation –
10x2– 31x – 14 =0
or, 10x2– 35x + 4x – 14 = 0
or, 5x (2x – 7) + 2 (2x – 7) = 0
or, (5x + 2) (2x – 7) = 0
or, x = – 2/5 or 7/2
Second equation –
5y2– 8y – 4 = 0
or, 5y2– 10y + 2y – 4 = 0
or, 5y (y – 2) + 2 (y – 2) = 0
or, (5y + 2) (y – 2) = 0
or, y = – 2/5 or 2
Now here x can be more than y, it can be equal to y or it can be less than y. So the answer is 5

7.Based on the equations given choose the option which is true :
I.  4x2– 1 = 0
II. 2y2 + 5y – 3 = 0

A. If x ≤ y

B. If x ≥ y

C. If x < y

D. If x > y

E. If x = y or no specific relation can be established

Show Correct Answers

E. If x = y or no specific relation can be established

First equation –
4x2– 1 = 0
or, x2 = ¼
so, x = ½ or – ½
Second equation –
2y2 + 5y – 3 = 0
or, 2y2 + 6y – y – 3 = 0
or, 2y (y + 3) – 1 (y + 3) = 0
or, (2y – 1) (y + 3) = 0
or, y = ½ or – 3
Here x can be more, less or equal to y so the answer is 5.

8.Based on the equations given choose the option which is true :

I. 3x2– 11x + 6 = 0
II. 2y2– 3y – 9 = 0

A. If x ≤ y

B. If x ≥ y

C. If x < y

D. If x > y

E. If x = y or no specific relation can be established

Show Correct Answers

E. If x = y or no specific relation can be established

First equation –
3x2– 11x + 6 = 0
or, 3x2– 9x – 2x + 6 = 0
or, 3x (x – 3) – 2 (x – 3) = 0
or, (3x – 2) (x – 3) = 0
or, x = 2/3 or 3
Second equation –
2y2– 3y – 9 = 0
or, 2y2– 6y + 3y – 9 = 0
or, 2y (y – 3) + 3 (y – 3) = 0
or, (2y + 3) (y – 3) = 0
or, y = 3 or – 3/2
Here, x can be more than y or less than y so the answer is 5.

9.Based on the equations given choose the option which is true :
I. 6x2– 11x + 3 = 0
II. 2y2– 7y + 6 = 0

A. If x ≤ y

B. If x ≥ y

C. If x < y

D. If x > y

E. If x = y or no specific relation can be established

Show Correct Answers

A. If x ≤ y

First equation –
6x2– 11x + 3 = 0
or, 6x2– 9x – 2x + 3 = 0
or, 3x (2x – 3) – 1 (2x – 3) = 0
or, (3x – 1) (2x – 3) = 0
or, x = 1/3 or 3/2
Second equation –
2y2– 7y + 6 = 0
or, 2y2– 4y – 3y + 6 = 0
or, 2y (y – 2) – 3 (y – 2) = 0
or, (2y – 3) (y – 2) = 0
or, y = 3/2 or 2
So here y is either equal to x or more than x.

10.Based on the equations given choose the option which is true :
I. 2x2 + 5x + 2 = 0
II. 4y2– 8y – 5 = 0

A. If x ≤ y

B. If x ≥ y

C. If x < y

D. If x > y

E. If x = y or no specific relation can be established

Show Correct Answers

A. If x ≤ y

First equation –
2x2 + 5x + 2 = 0
or, 2x2 + 4x + x + 2 = 0
or, 2x (x + 2) + 1 (x + 2) = 0
or, (2x + 1) (x + 2) = 0
or, x = – ½ or – 2
Second equation –
4y2– 8y – 5 = 0
or, 4y2– 10y + 2y – 5 = 0
or, 2y (2y – 5) + 1 (2y – 5) = 0
or, (2y + 1) (2y – 5) = 0
or, y = – ½ or 5/2
So here y is always more than x or equal to x.


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