**Hello Aspirants**. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating sample questions in **Quadratic Equations** which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

Follow the link **To solve Quadratic Equations with the help of Number Line**

**30x**^{2}+ 11x + 1 = 0

**42y**^{2}+ 13y + 1 = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**D. X ≤ Y**

Explanation:

30x^{2}+ 11x + 1 = 0

30x^{2}+ 6x + 5x + 1 = 0

x = – 0.16, -0.19

42y^{2}+ 13y + 1 = 0

42y^{2}+ 6y + 7y + 1 = 0

y = -0.14, -0.16

Put on number line

-0.19, -0.16, -0.16, -0.14**x**^{2}– x – √2x + √2= 0

**y**^{2}– 3y + 2 = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

x^{2}– x – √2x + √2= 0

x (x-1) – √2(x -1) = 0

(x-1) (x-√2) = 0

x = 1, 1.414

y^{2}– 3y + 2 = 0

y^{2}– y – 2y + 2 = 0

y = 1, 2

Put on number line

1, 1, 1.414, 2**x**^{2}– 2x – √5x + 2√5 = 0

**y**^{2}– √3y – √2y + √6 = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**A. X > Y**

Explanation:

x^{2}– 2x – √5x + 2√5= 0

x (x-2) – √5(x-2) = 0

(x-2) (x-√5) = 0

x = 2, 2.23

y^{2}– √3y – √2y + √6 = 0

y (y-√3) – √2(y-√3) = 0

(y-√2) (y-√3) = 0

y = 1.414, 1.732

Put on number line

1.414, 1.732, 2, 2.23**x**^{2}+ 12x + 36 = 0

**y**^{2}= 16

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**B. X < Y**

Explanation:

x^{2}+ 12x + 36 = 0

x^{2}+ 6x + 6x + 36 = 0

x = -6, -6

y^{2}= 16

y = ± 4

Put on number line

-6, -6, -4, 4**9x**^{2}+ 3x – 2 = 0

**8y**^{2}+ 6y + 1 = 0

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

9x^{2}+ 3x – 2 = 0

9x^{2}+ 6x -3x – 2 = 0

x = 0.33, -0.66

8y^{2}+ 6y + 1 = 0

8y^{2}+ 4y + 2y + 1 = 0

y = -0.25, -0.5

Put on number line

-0.66, -0.5,-0.25,0.33**3x² + 11x + 6 = 0**

**3y² + 10y + 8 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

3x² + 11x + 6 = 0

3x² + 9x + 2x + 6 = 0

x = -0.66, -3

3y² + 10y + 8 = 0

3y² + 6y + 4y + 8 = 0

y = -1.33, -2

Put on number line

-3, -2, -1.33, -0.66**3x² – 7x + 2 = 0**

**2y² – 9y + 10 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**D. X ≤ Y**

Explanation:

3x² – 7x + 2 = 0

3x² -x -6x + 2 = 0

x = 2, 0.33

2y² – 9y + 10 = 0

2y² – 4y -5y + 10 = 0

y = 2.5, 2

Put on number line

0.33, 2, 2, 2.5**x² = 9**

**2y² – 19y + 44 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**B. X < Y**

Explanation:

x² = 9

x = ± 3

2y² – 19y + 44 = 0

2y² – 11y – 8y + 44 = 0

y = 5.5, 4

Put on number line

-3, 3, 4, 5.5**2x² -15x + 28 = 0**

**4y² – 23y + 30 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**E. X = Y or relation cannot be established**

Explanation:

2x² -15x + 28 = 0

2x² -8x -7x + 28 = 0

x = 4, 3.5

4y^{2}– 23y + 30 = 0

4y^{2}– 15y – 8y + 3 = 0

y = 3.75, 2

Put on number line

2, 3.5, 3.75, 4**2x² -15x + 27 = 0**

**5y² – 26y + 33 = 0**

A. X > Y

B. X < Y

C. X ≥ Y

D. X ≤ Y

E. X = Y or relation cannot be established

**C. X ≥ Y**

Explanation:

2x² -15x + 27 = 0

2x² -6x -9x + 27 = 0

x = 3, 4.5

5y² – 26y + 33 = 0

5y² – 11y – 15y + 33 = 0

y = 3, 2.2

Put on number line

2.2, 3, 3, 4.5

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