If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
Solution and Explanation
Let the root of the quadratic equation be a and b.
According to the given condition,
\(A.M. = \frac{a + b }{ 2} = 8 ⇒ a + b = 16 ...(1)\)
\(G.M. = \sqrt{ab} = 5 ⇒ab = 25 ...(2)\)
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 x 2 -16x + 25 = 0.
Top Questions on relationship between a.m. and g.m.
- The product of n positive numbers is unity, then their sum is :
- BITSAT - 2014
- Mathematics
- relationship between a.m. and g.m.
- Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of
- KEAM
- Mathematics
- relationship between a.m. and g.m.
- If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A±√(A+G)(A-G).
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
- What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
- CBSE Class XI
- Mathematics
- relationship between a.m. and g.m.
Questions Asked in CBSE Class XI exam
(i) List the deeds that led Ray Johnson to describe Akhenaten as “wacky”.
(ii) What were the results of the CT scan?
(iii) List the advances in technology that have improved forensic analysis.
(iv) Explain the statement, “King Tut is one of the first mummies to be scanned — in death, as in life...”- CBSE Class XI
- Discovering Tut: The saga Continues
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
- Discovering Tut: The saga Continues
- Write a note on economic importance of algae and gymnosperms.
- CBSE Class XI
- Bryophytes
- Briefly comment on "The author’s meeting with Norbu."
- CBSE Class XI
- Silk road
- The story revolves around characters who belong to a tribe in Armenia. Mourad and Aram are members of the Garoghlanian family. Now locate Armenia and Assyria on the atlas and prepare a write-up on the Garoghlanian tribes. You may write about people, their names, traits, geographical and economic features as suggested in the story.
- CBSE Class XI
- The summer of the beautiful white horse
Concepts Used:
Sequence and Series
Sequence: Sequence and Series is one of the most important concepts in Arithmetic. A sequence refers to the collection of elements that can be repeated in any sort.
Eg: a1,a2,a3, a4…….
Series: A series can be referred to as the sum of all the elements available in the sequence. One of the most common examples of a sequence and series would be Arithmetic Progression.
Eg: If a1,a2,a3, a4……. etc is considered to be a sequence, then the sum of terms in the sequence a1+a2+a3+ a4……. are considered to be a series.
Types of Sequence and Series:
Arithmetic Sequences
A sequence in which every term is created by adding or subtracting a definite number to the preceding number is an arithmetic sequence.
Geometric Sequences
A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.
Harmonic Sequences
A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.
Fibonacci Numbers
Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fn = Fn-1 + Fn-2