Kit Library / Mathematics / Algebra
⚡ Topic Learning KitQuadratic Equations
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Quadratic Equations
Quadratic equations are second-degree polynomial equations of the form $ax^2 + bx + c = 0$ with $a \neq 0$. They model parabolic relationships and can be solved by factoring, completing the square, or the quadratic formu…
- A quadratic equation is any equation of the form $ax^2 + bx + c = 0$ with $a \neq 0$.
- Three common solving methods: factoring, completing the square, and the quadratic formula.
- The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ works for all quadratics.
~8 min · full explanation, examples & memory tricks in the app
Try the smart MCQs from this kit
15 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Which of the following is a quadratic equation?
BeginnerShow answer & explanation
$x^2 - 5x + 6 = 0$
A quadratic equation is of the form $ax^2 + bx + c = 0$ with $a \neq 0$. Only $x^2 - 5x + 6 = 0$ fits this form.
What is the standard form of a quadratic equation?
BeginnerShow answer & explanation
$ax^2 + bx + c = 0$
The standard form of a quadratic equation in variable $x$ is $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and $a \neq 0$.
The roots of the quadratic equation $x^2 - 7x + 12 = 0$ are:
IntermediateShow answer & explanation
$3$ and $4$
Factorising: $x^2 - 7x + 12 = (x-3)(x-4) = 0$, so $x = 3$ or $x = 4$.
The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is:
BeginnerShow answer & explanation
$b^2 - 4ac$
The discriminant, denoted by $D$ or $\Delta$, is $b^2 - 4ac$. It determines the nature of the roots.
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