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What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
Concept: Nature of Roots of a Quadratic Equation
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
Concept: Nature of Roots of a Quadratic Equation
Complete the following activity to solve the given quadratic equation by formula method.
2x2 + 13x + 15 = 0
Activity: 2x2 + 13x + 15 = 0
a = (______), b = 13, c = 15
b2 – 4ac = (13)2 – 4 × 2 × (______)
= 169 – 120
b2 – 4ac = 49
x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`
x = `(- ("______") +- sqrt(49))/4`
x = `(-13 +- ("______"))/4`
x = `(-6)/4` or x = `(-20)/4`
x = (______) or x = (______)
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
Concept: Nature of Roots of a Quadratic Equation
If `(5sqrt(2) + 3sqrt(3)) - (6sqrt(2) - 7sqrt(3)) = asqrt(2) + bsqrt(3)`, then find a and b.
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
Solve: 7x2 – 30x – 25 = 0
Concept: Method of Solving a Quadratic Equation >> Quadratic Formula (Shreedharacharya's Rule)
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 (nth) 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
