Quadratic Equations — Part 2: The discriminant and problems that lead to quadratics: visual lesson, ICSE Class 10 Mathematics

Lesson

Quadratic Equations, Part 2

Before solving, one number tells you how many real roots to expect.

In this lesson you will

Use the discriminant to decide the nature of the roots
Find a parameter for which a quadratic has equal roots
Form quadratic equations from problems on numbers, area, speed, time, age and work
Reject roots that do not fit the problem

Two crossings: two real, distinct roots.

Concept

Concept

In the formula, $b^2 - 4ac$ sits under the square root. It is called the discriminant, $D$ .

The sign of $D$ decides the nature of the roots.
Discriminant $D = b^2 - 4ac$	Nature of roots	Example	$D$
$D > 0$	two real, distinct (unequal) roots	$x^2 - 6x + 5 = 0$	$16$
$D = 0$	two real, equal roots, each $-\dfrac{b}{2a}$	$x^2 - 6x + 9 = 0$	$0$
$D < 0$	no real roots	$x^2 - 6x + 10 = 0$	$-4$