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 of all numbers between 200 and 400 which are divisible by 7.
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).
Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
Find the derivative of x2 – 2 at x = 10.
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
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where is the 30th sum???????????? of exercise 2 in sequences and series
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