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Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
Concept: Nature of Roots of a Quadratic Equation
Solve the quadratic equation: 16x2 + 24x + 9 = 0.
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
Solve the quadratic equation 7x2 + 9x + 2 = 0 by the quadratic formula.
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
Solve the following quadratic equation by the formula method:
x2 + 10x + 2 = 0
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
Solve the following quadratic equation by formula method:
3m2 − m − 10 = 0
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24th term of this progression.
Concept: General Term of an Arithmetic Progression
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
For an given A.P., t7 = 4, d = −4, then a = ______.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Six year before, the age of mother was equal to the square of her son's age. Three year hence, her age will be thrice the age of her son then. Find the present ages of the mother and son.
Concept: General Term of an Arithmetic Progression
Simplify `sqrt(50)`
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
What is the sum of first 10 terms of the A. P. 15,10,5,........?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
