Page 19 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

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Where D=b -4ac is the discriminant. i.e. if α & β are two roots of the
given quadratic equation then

α= -b±√D and β= -b-√D
2a 2a

Properties of Quadratic Equations

• A quadratic equation has two and only two roots.

• A quadratic equation cannot have more than two different roots.

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• If a be a root of the quadratic equation ax +bx+c=0, a≠0 , then (x-α)

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is a factor of ax +bx+c=0, a≠0,then

Sum and Product of the roots of a Quadratic Equation

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Let α, β be the roots of a quadratic equation ax + bx + c=0, a≠0 then

c
α+β= -b =- ( coefficient of x ) and α.β= = ( constant term )
a coefficient of x 2 a coefficient of x 2
Formation of a Quadratic Equation

Let α, β be the two roots then we can form a quadratic equation as

follows

X - (sum of roots) x + (product of roots) = 0
2

or (x - a) (x -β) =0 or (x-α)(x-β)=0

Therefore,

• If the roots a and ß reciprocal to each other, then a = c.

• If the two roots a and be equal in magnitude and opposite in sign

b=0.

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