Additional Mathematics

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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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