Relationship of Zeroes With Coefficients Of Quadratic Polynomial:
If (read as alpha) is a zero of p(x) then
If and ( read as beta) are two zeroes of p(x) then
We can use these reltaions to obtain values of several symmetric expressions involving and in terms of a, b and c.
An expressons in and is said to be symmetric if it remaiins unchanged when and are intercharged. For instance, and are symmetric expressions in and .
Example: If a and c are such that the quadratic polynomial has 10 as the sum of zeroes and also as the product of zeroes, fiind a and c.
Solution: Let be the zeroes of Then
As we get
and c = 10a = 5
Thus,
Example : If and are zeros of the quadratic polynomial . find the value of
Solution:
We first find We have
Next
Thus,
Example: If are zeros of then obtain quadratic polynomials whose zeros are
Solution: As are zeros of
Thus, the quadratic expression whose zeros are is
or
or
If are zeros of then obtain quadratic polynomials whose zeros are
| |||
Right Option : A | |||
View Explanation |
If one zero of the quadratic polynomial is 2, find the value of k. Also, find the other zero of the polynomial. | |||
Right Option : C | |||
View Explanation |
Quadratic equation whose one of the roots is is: | |||
Right Option : D | |||
View Explanation |
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.
Abhyas 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.
A 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.
My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
It 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.
It 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
I 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
My 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.
Being 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.
About 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.