If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
Let the root of the quadratic equation be a and b.
According to the given condition,
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
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Find the sum to n terms in the geometric progression 1,-a, a2,-a3, ... (if a ≠ -1)
Find the derivative of x at x = 1.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
For what values of x, the numbers are in G.P?
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
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’
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.
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where is the 30th sum???????????? of exercise 2 in sequences and series
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