Page 10 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

2(3±√5)
= =3±√5
2

Thus the roots of the equation are 3+√5 & 3-√5.

D. Determining Nature of Roots of the Quadratic

Equation:

Let the quadratic equation is ax²+bx+c=0, …… (i)

Where a≠0 and a, b, c ∈ R.

Roots of the given quadratic equation are x= -b±√D ,
2a

Where D = b² – 4ac is called discriminant.

So, if are two roots of the quadratic equation (i). Then,

-b+√D -b-√D
α= and β=
2a 2a

Now, the following cases are possible.

Case-I: When D > 0,

Roots are real and unequal (distinct).

The roots are given by α= -b+√D and β= -b-√D
2a 2a

Remark:

Consider a quadratic equation ² + + = 0, where a, b, c ∈ Q, a≠0

and D > 0 then:

Case l:

If D is a perfect square, then roots are rational and unequal.

If D is not a perfect square, then roots are irrational and unequal. If

one root is of the from p + q (where p is rational, and q is a surd),
√
√
then the other root will help p – q.
√

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