Quadratic Equations — Part 1: Solving by factorisation and by formula: visual lesson, ICSE Class 10 Mathematics

Lesson

Quadratic Equations, Part 1

A quadratic equation has at most two roots. On a graph, they are where the parabola meets the $x$ -axis.

In this lesson you will

Write a quadratic equation in standard form and read off a, b and c
Solve a quadratic equation by splitting the middle term
Solve a quadratic equation by the quadratic formula
Give roots in surd form, to a stated number of decimal places or to significant figures

The roots of $x^2 + x - 12 = 0$ are where the graph meets the $x$-axis: $-4$ and $3$.

Concept

Write any quadratic in standard form $ax^2 + bx + c = 0$
Solve by splitting the middle term
Solve by the quadratic formula
Give roots in surd form, to decimal places or to significant figures

Concept

A quadratic equation in $x$ can be written as $ax^2 + bx + c = 0$ , where $a$ , $b$ , $c$ are real numbers and $a \ne 0$ .

Always simplify first, then read $a$, $b$ and $c$ with their signs.
Equation	Standard form	$a$ , $b$ , $c$	Quadratic?
$3x^2 - 5x = 2$	$3x^2 - 5x - 2 = 0$	$3,\ -5,\ -2$	yes
$x(x - 4) = 7$	$x^2 - 4x - 7 = 0$	$1,\ -4,\ -7$	yes
$5 - 2x^2 = 0$	$2x^2 - 5 = 0$	$2,\ 0,\ -5$	yes
$(x + 2)^2 = x^2 + 9$	$4x - 5 = 0$	—	no: the $x^2$ terms cancel