What Makes an Equation Quadratic?
Degree 2 is the whole game.
↳ If a = 0, the equation collapses to linear — so a ≠ 0 is the defining condition.
Kit Library / Mathematics / Algebra
⚡ Topic Learning KitQuadratic Equations
English 19 leveled MCQs 25 flashcards 9 games Free
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➗ Formula
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Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
The Quadratic Formula: Your Universal Solver
One formula solves every quadratic.
↳ Memorise this formula — it is the fallback when factorisation fails.
The Discriminant Tells You the Nature of Roots
One number predicts your roots.
↳ Compute D first — it tells you what kind of answer to expect before solving.
📖 Smart notes
What you'll study, topic by topic
1
Quadratic Equations
Quadratic equations are polynomial equations of degree two, written in the standard form ax² + bx + c = 0 where a ≠ 0. They can be solved by factorisation, completing the square, or the quadratic formula, and their roots...
- A quadratic equation has the standard form $ax^2 + bx + c = 0$ where $a \neq 0$.
- The condition $a \neq 0$ is essential — otherwise the equation becomes linear.
- The quadratic formula is $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
~18 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
19 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Which of the following is the standard form of a quadratic equation?
Beginner
A $a^2x + b = 0$
B $ax + b = 0$
C $ax^2 + bx + c = 0$
D $ax^3 + bx^2 + cx + d = 0$
Show answer & explanation
$ax^2 + bx + c = 0$
A quadratic equation has the form $ax^2 + bx + c = 0$ with $a \neq 0$. The highest power of the variable must be 2.
In the equation $ax^2 + bx + c = 0$, which condition must hold for it to be quadratic?
Beginner
A $a = 0$
B $c \neq 0$
C $b = 0$
D $a \neq 0$
Show answer & explanation
$a \neq 0$
If $a = 0$, the $x^2$ term vanishes and the equation becomes linear. The condition $a \neq 0$ is essential.
What is the discriminant of a quadratic equation $ax^2 + bx + c = 0$?
Beginner
A $4ac - b^2$
B $b^2 + 4ac$
C $\sqrt{b^2 - 4ac}$
D $b^2 - 4ac$
Show answer & explanation
$b^2 - 4ac$
The discriminant is $D = b^2 - 4ac$. It is the expression under the square root in the quadratic formula.
If the discriminant $D > 0$, what can you say about the roots?
Beginner
A No real roots
B Two distinct real roots
C Exactly one real root
D Two equal real roots
Show answer & explanation
Two distinct real roots
When $D > 0$, the square root is a positive real number, giving two different real values for $x$.
🃏 Flashcards
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25 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
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Memory Match
Flashcard Battle
Speed Quiz
Guess Term
Sequence Builder
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