Solve the following quadratic equation for x: `4x^2 + 4bx – (a^2 – b^2) = 0`

Concept: Solutions of Quadratic Equations by Completing the Square

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence

If α + β = 5 and α^{3} +β^{3} = 35, find the quadratic equation whose roots are α and β.

Concept: Quadratic Equations

If the quadratic equation px^{2} − 2√5px + 15 = 0 has two equal roots then find the value of p.

Concept: Nature of Roots

If 12x +13y =29 and 13x +12y=21, find x + y.

Concept: Linear Equations in Two Variables Applications

Write the first two terms of the sequence whose nth term is t_{n} = 3n ‒ 4.

Concept: Arithmetic Progression

The 11^{th} term and the 21^{st} term of an A.P. are 16 and 29 respectively, then find:

(a) The first term and common difference

(b) The 34^{th} term

(c) ‘n’ such that t_{n} = 55

Concept: Arithmetic Progression

Find the term t15 of an A.P. : 4, 9, 14, …………..

Concept: General Term of an Arithmetic Progression

State whether the following sequence is an Arithmetic Progression or not:

3, 6, 12, 24,......

Concept: Arithmetic Progression

Find n if the nth term of the following A.P. is 68

5, 8, 11, 14, ..........

Concept: Arithmetic Progression

The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.

a = 5, d = 4, s12 = ?

`s_n = n/2 [ square ]`

`s_12 = 12/2 [10 +square]`

`= 6 × square `

` =square`

Concept: Sum of First n Terms of an AP

Write the quadratic equation whose roots are ‒2 and ‒3.

Concept: Quadratic Equations

Solve the following quadratic equation by using formula method: 5m^{2} + 5m – 1 = 0

Concept: Nature of Roots

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Concept: Quadratic Equations Examples and Solutions

Solve the following quadratic equation by factorization method : `x^2-5x+6=0`

Concept: Solutions of Quadratic Equations by Factorization

Solve the following quadratic equation by factorization method : `3x^2-29x+40=0`

Concept: Solutions of Quadratic Equations by Factorization

State whether the given equation is quadratic or not. Give reason.

`5/4m^2 - 7 = 0`

Concept: Quadratic Equations

If one of the roots of the quadratic equation x^{2} - 11x + k = 0 is 9, then find the value of k

Concept: Quadratic Equations Examples and Solutions

Factorise : m^{2} + 5m + 6.

Concept: Solutions of Quadratic Equations by Factorization

Solve the following simultaneous equations: `7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33`

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables