Quadratic Equation – Definition, Formulas, How to Solve Algebra Problems? (Video Lessons)

Definition and Formulas for Quadratic Equation (Algebra)

1. Def. of Quadratic Equation: Quadratic Equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b and c are real numbers.
2. (a+b)² = a² + b² + 2ab
   or it can also be written as:
   (a+b)² = (a-b)² + 4ab
3. (a-b)² = a² + b² – 2ab
   or it can also be written as:
   (a-b)² = (a+b)² – 4ab
4. (a+b)³ = a³ + b³ + 3ab(a+b) = a³ + b³ + 3a²b + 3ab²
5. (a-b)³ = a³ – b³ – 3ab(a-b) = a³ – b³ – 3a²b + 3ab²
6. a³ + b³ = (a+b)³ – 3ab(a+b)
   or it can also be written as:
   a³ + b³ = (a+b) (a²-ab+b²)
7. a³ – b³ = (a-b)³ + 3ab(a-b)
   or it can also be written as:
   a³ – b³ = (a-b) (a²+ab+b²)
8. a² – b² = (a-b)(a+b)
9. a^m * aⁿ = a^m+n
10. a^m / aⁿ = a^m-n
11. (a/b)^(m/n) = (b/a)^-(m/n)
12. a^m / b^-n = a^m * bⁿ

Aptitude Questions on Quadratic Equations (Algebra) with Solved Examples

Q.1: x² – 34x + 288 = 0
y² – 28y + 192 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: C. X ≥ Y
Explanation:
x² – 34x + 288 = 0
x = 18, 16
y² – 28y + 192 = 0
y = 12, 16

Q.2: x² – 26x + 168 = 0
y² – 32y + 252 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: D. X ≤ Y
Explanation:
x² – 26x + 168 = 0
x = 12, 14
y² – 32y + 252 = 0
y = 14, 18

Q.3: x² + 26x + 168 = 0
y² + 23y + 132 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: D. X ≤ Y
Explanation:
x² + 26x + 168 = 0
x = -12, -14
y² + 23y + 132 = 0
y = -12, -11

Q.4: x² – 44x + 448 = 0
y² – 28y + 195 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: A. X > Y
Explanation:
x² – 44x + 448 = 0
x = 28, 16
y² – 28y + 195 = 0
y = 13, 15


Q.5: x² – 26x + 168 = 0
y² – 34y + 285 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: B. X < Y
Explanation:
x² – 26x + 168 = 0
x = 12, 14
y² – 34y + 285 = 0
y = 15, 19

Q.6: x² – 38x + 352 = 0
y² – 25y + 154 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: A. X > Y
Explanation:
x² – 38x + 352 = 0
x = 22, 16
y² – 25y + 154 = 0
y = 11, 14

Q.7: x² = 121
y² – 46y + 529 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: B. X < Y
Explanation:
x² = 121
x = 11, – 11
y² – 46y + 529 = 0
y = 23, 23

Q.8: x² + 29x + 208 = 0
y² + 19y + 78 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: D. X ≤ Y
Explanation:
x² + 29x + 208 = 0
x = -13, -16
y² + 19y + 78 = 0
y = -13, -6


Q.9: x² – 41x + 400 = 0
y² – 29y + 210 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: A. X > Y
Explanation:
x² – 41x + 400 = 0
x = 25, 16
y² – 29y + 210 = 0
y = 14, 15

Q.10: x² – 25x + 156 = 0
y² – 32y + 255 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
Answer: B. X < Y
Explanation:
x² – 25x + 156 = 0
x = 12, 13
y² – 32y + 255 = 0
y = 15, 17