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If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respect...

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

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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!!!ð§ð§ð§

sumaiya
2016-10-30 11:26:24

If u have any problem then go to saral study. Com Thanks a lot

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

This is so helpful ! Thank you

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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....

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

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