# QUADRATIC EQUATION - NATURE OF ROOTS - ROOTS UNDER PARTICULAR CASES

**QUADRATIC EQUATION - NATURE OF ROOTS - ROOTS UNDER PARTICULAR CASES**

Let the quadratic equation has real roots and

a. if b = 0 then roots are equal in magnitude but opposite in sign

b. if c = 0. then one root is zero other is – b/a

c. if a = c then roots are reciprocal to each other

d. If a+b+c=0 i.e one root is 1 and second root is c/a or(–b–a)/a.

e. if sign of a = sign of b != sign of c then Greater root in magnitude is negative

f. if sign of b = sign of c != sign of a then Greater root in magnitude is positive

** Example : **

If equation has roots equal in magnitude & opposite in sign, then the value of k is?

**Solution :**

**Example **

If roots of the equation (a–b)x2 +(c–a)x+(b–c)=0 are equal,then a,b,c are in.

**Solution**

Sum of the coefficients = 0

Hence one root is 1 and other root is

Given that both roots are equal, so

Hence a, b, c are in A.P.