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 :

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

 

 

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.

 

Post By : Rahul Kumar 07 Apr, 2020 1832 views Maths