Nature of Roots of Quadratic Polynomial
Nature of Roots of Quadratic Polynomial
Nature of Roots of Quadratic Polynomial:
The Value of Discriminant decides the nature of roots of a quadratic Polynomial.
Case 1: If , then the roots are real and equal
Case 2: If , then the roots are real and unequal.
Case 3: If , then the roots are imaginary
Example: Without solving the equation identify the nature of roots
Solution: Comparing the equation with the standard form
a = 2, b = 5 and c = 5, Then
As the discriminant is less than zero so the roots are imaginary
Example: Find the value of k for which the equation has real and equal roots
Solution: Comparing the equation with the standard form
a = 1, b = -2(1+3k) and c = 7(3+2k), Then
As the roots are real and equal, so D = 0
The number of real roots of equation: | |||
| Right Option : C | |||
| View Explanation | |||
| |||
| Right Option : B | |||
| View Explanation | |||
Find the nature of the roots of | |||
| Right Option : B | |||
| View Explanation | |||
Students / Parents Reviews [10]
One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
