Types of Roots of Quadratic Equations

Additional Mathematics

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Types of Roots of Quadratic Equations

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Discriminant

If the discriminant b^2–4ac > 0,

The equation has two different real roots

If the discriminant b^2–4ac=0,

The equation has two equal real roots

If the discriminant b^2–4ac < 0,

The equation has no real roots

Square root of a negative number is known as imaginary root

Reason why we must calculate the value of the discriminant first before determining the types of roots of a quadratic equation

This information is helpful because it serves as a double check when solving quadratic equations by any of the two methods (completing the square and using the quadratic formula)

Line y=mx+c touches a point on the curve

The equation has two equal real roots

Line y = mx + 4 crosses a curve at two points

The equation has two different real roots

Line y = mx+c does not cross the curve

The equation has no real roots.

Use of discriminant

(a) Find the value of a variable in the quadratic equation (b) Derive a relation

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Types of Roots of Quadratic Equations

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