Question 32

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,

The quadratic equation is given by,

*x*^{2}– *x* (Sum of roots) + (Product of roots) = 0

*x*^{2} – *x* (*a* + *b*) + (*ab*) = 0

*x*^{2} – 16*x* + 25 = 0 [Using (1) and (2)]

Thus, the required quadratic equation is *x*^{2} – 16*x* + 25 = 0

- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

- Q:-
How many terms of G.P. 3, 3

^{2}, 3^{3}, … are needed to give the sum 120? - Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.

- Q:- Write the following sets in roster form:

(i) A = {x: x is an integer and - 3 < x < 7}.

(ii) B = {x: x is a natural number less than 6}.

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

(iv) D = {x: x is a prime number which is divisor of 60}.

(v) E = The set of all letters in the word TRIGONOMETRY.

(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

- Q:-
Find the sum to

*n*terms of the series 3 × 1^{2}+ 5 × 2^{2}+ 7 × 3^{2}+ … - Q:-
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

- Q:-
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio

- Q:-
Describe the sample space for the indicated experiment: A coin is tossed three times.

- Q:-
Prove the following by using the principle of mathematical induction for all n ∈ N:

n (n + 1) (n + 5) is a multiple of 3.

- Q:-
Find the sum to

*n*terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + … - Q:-
A die is thrown. Describe the following events:

(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3

(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3

Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F’, F’

- Q:-
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).

- Q:-
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

- Q:-
Given a G.P. with

*a*= 729 and 7th term 64, determine S_{7}.

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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