If A.M. and G.M. of roots of a quadratic | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

Answer:

Let the root of the quadratic equation be a and b.

According to the given condition,

A. M. space equals fraction numerator a plus b over denominator 2 end fraction equals 8 rightwards double arrow a plus b space equals space 16 space space space space space space space space space space space space space.... left parenthesis 1 right parenthesis
G. M. space equals space square root of a b end root space equals space 5 space rightwards double arrow a b space equals space 25 space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

The quadratic equation is given by,

x2– x (Sum of roots) + (Product of roots) = 0

x2 – x (a + b) + (ab) = 0

x2 – 16x + 25 = 0 [Using (1) and (2)]

Thus, the required quadratic equation is x2 – 16x + 25 = 0


Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

  • Read the question carefully and focus on the core concept being asked.
  • Reference examples and data from the chapter when answering questions about Sequence and Series.
  • Review previous year question papers to get an idea of how such questions may be framed in exams.
  • Practice answering questions within the time limit to improve your speed and accuracy.
  • Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

  • lechu
  • 2017-11-05 17:23:58

thank you for this


  • Meghana
  • 2017-09-24 19:28:46

where is the 30th sum???????????? of exercise 2 in sequences and series


  • Riya
  • 2017-08-25 21:42:39

Very helpful!!!👧👧👧


  • sumaiya
  • 2016-10-30 11:26:24

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  • Shreya Srinivas
  • 2015-07-20 21:09:57

This is so helpful ! Thank you


Comment(s) on this Question

Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 32: If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadrat....