Q. 14.2( 216 Votes )

Find the nature o

Answer :

There are three types of roots that are possible for a quadratic equation:

For a quadratic equation: a x2 + b x + c = 0, we know that its roots is given by the formula




(i) Comparing this equation with ax2 + bx + c = 0, we obtain,


a = 2, b = −3, c = 5


Discriminant D = b2 − 4ac = (− 3)2 − 4 (2) (5) = 9 − 40 = −31


As, b2 − 4ac < 0,


Therefore, no real root is possible for the given equation.


(ii) Comparing this equation with ax2 + bx + c = 0,


we obtain,


a = 3


b = -4√3


c = 4



Discriminant = 48 − 48 = 0


As, b2 − 4ac = 0,


Therefore, real roots exist for the given equation and they are equal to each other.


And the roots will be and .



Therefore, the roots are and .


(iii) Comparing this equation with ax2+bx + c = 0,


we obtain,


a = 2, b = −6, c = 3


Discriminant = b2 − 4ac = (− 6)2 − 4 (2) (3) = 36 − 24 = 12


As, b2 − 4ac > 0,


Therefore, distinct real roots exist for this equation as follows.






So, the roots are or .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses