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MCQ Practice
Quadratic Equations — MCQ Practice
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Lesson
Quadratic Equations — Complete Lesson
?? What is a Quadratic Equation?
A quadratic equation is of the form: ax² + bx + c = 0, where a ? 0.
?? Think of it like a Bollywood plot: The hero (x) must find two secret values (roots) that solve the mystery equation. Sometimes both are real, sometimes they don't exist (imaginary)!
?? Methods to Solve
- Factorisation: Split middle term and factor
- Completing the Square: Make it a perfect square
- Quadratic Formula: x = (-b ± v(b²-4ac)) / 2a
?? Discriminant (D = b² - 4ac)
| Discriminant | Nature of Roots |
|---|---|
| D > 0 | Two distinct real roots |
| D = 0 | Two equal real roots |
| D < 0 | No real roots |
?? Example
Solve: x² - 5x + 6 = 0
Factoring: (x - 2)(x - 3) = 0
x = 2 or x = 3 ?
Using formula: a=1, b=-5, c=6
D = 25 - 24 = 1 > 0 ? two roots
x = (5 ± 1)/2 = 3 or 2 ?
Factoring: (x - 2)(x - 3) = 0
x = 2 or x = 3 ?
Using formula: a=1, b=-5, c=6
D = 25 - 24 = 1 > 0 ? two roots
x = (5 ± 1)/2 = 3 or 2 ?
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Memory Trick
Quadratic Equations — Mnemonic
Mnemonic 1: Quadratic Formula Fun 🎉
"X equals minus B, plus-minus root, B square minus 4AC, all over 2A"
Hindi rhyme to remember:
“Minus B le, plus minus root, B square minus 4AC ka jhoot, sabko 2A se baant do, x ki value mil jaayegi yaar!” 😄
Mnemonic 2: FACTORING Made Easy 🧩
- Find two numbers whose Product = a × c and Sum = b
- Arrange the middle term using these two numbers
- Common factor take out from pairs
- Take common binomial factor
- Observe and write factors
- Remember: Practice makes perfect!
Mnemonic phrase: “F-A-C-T-O-R” = Find Arrange Common Take Observe Remember 📚
Mnemonic 3: Roots Relation Trick 🌱
Sum of roots = -b/a, Product of roots = c/a
Hindi phrase to recall:
“Minus B ko A se bhaag do, mil jaaye roots ka yog, C ko A se bhaag ke, milta hai roots ka gun.” 🎯
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