Pythagoras Theorem – Exercise 12.1 – Questions: a. Numerical problems based on Pythagoras theorem. The sides of a right angled triangle containing the right angle are 5 cm and 12 cm, find its hypotenuse. Find the length often diagonal of a square of side 12 cm. The length of the diagonal of a rectangular playground… Continue reading Pythagoras Theorem Exercise 12.1 – Class 10

# Tag: Karnataka state syllabus class 10

## Quadratic Equations Exercise 9.9 – Class X

Quadratic Equations – Exercise 9.9 – Question: Draw the graphs of the following quadratic equations: (i) y = - x2 (ii) y = 3x2 (iii) y = 1/2 x2 – 2 (iv) y = x2 – 2x (v) y = x2 – 8x + 7 (vi) y = (x + 2)(2 – x) (vii) y… Continue reading Quadratic Equations Exercise 9.9 – Class X

## Quadratic Equation – Exercise 9.6 – Class X

So far we have learnt to find the roots of given quadratic equations by different methods. We see that the roots are all real numbers. Is it possible to determine the nature of roots of a given quadratic equation, without actually finding them? Now, let us learn about this. Nature of the roots of quadratic… Continue reading Quadratic Equation – Exercise 9.6 – Class X

## Quadratic Equations – Exercise 9.5 – Class X

We know that, in mathematics calculations and solving problems are made easier by using formulae. In the same way, quadratic equation can be easily solved by using a formula. The quadratic formula, which is very useful for finding its roots can be derived using the method of completing the square. Let us derive the quadratic… Continue reading Quadratic Equations – Exercise 9.5 – Class X

## Quadratic Equations – Exercise 9.4 – Class X

Solving Quadratic Equations by Completing the Square Method: Let us consider the quadratic equation by completing the square equation, x2 + 5x + 5 = 0. Here in the middle tem 5x cannot split into terms such that m + n = 5 and mn = 5. This means we cannot resolve the equation as… Continue reading Quadratic Equations – Exercise 9.4 – Class X

## Quadratic equations – Exercise 9.3 – Class X

Solutions of adfected Quadratic equations - Quadratic Equations: We know the general form of an adfected quadratic equation is ax² + bx + c, a≠0. this equation can also occur in different forms such as ax² + bx = 0, ax² + c = 0, and ax² = 0. Solution of a quadratic equation by factorisation method -… Continue reading Quadratic equations – Exercise 9.3 – Class X

## Quadratic Equations – Exercise 9.2 – Class X

Previous Exercise - Quadratic Equations – Exercise 9.1 – Class X Quadratic equations – Exercise 9.2 1.Classify the following equations into pure and adfected quadratic equations: (i) x2 = 100 (ii) x2 + 6 = 100 (iii) p(p – 3) = 1 (iv) x3 + 3 = 2x (v) (x+ 9)(x – 9) = 0… Continue reading Quadratic Equations – Exercise 9.2 – Class X

## Quadratic Equations – Exercise 9.1 – Class X

Quadratic Equations – Exercise 9.1 Check whether the following are quadratic equations: (i) x2 – x = 0 (ii) x2 = 8 (iii) x2 + 1/2 x = 0 (iv) 3x – 10 = 0 (v) x2 – 29/4 x + 5 = 0 (vi) 5 – 6x = 2/5x2 (vii) √2x2 + 3x =… Continue reading Quadratic Equations – Exercise 9.1 – Class X

## Polynomials – Exercise 8.5 – Class X

Previous Exercise - Polynomials – Exercise 8.4 – Class X Polynomials – Exercise 8.5 Find the quotients and remainder using synthetic division. (i) (x3 + x2 – 3x + 5) /(x – 1) (ii) (3x3 – 2x2 + 7x - 5) /(x + 3) (iii) (4x3 – 16x2 – 9x – 36)/(x + 2) (iv) (6x4… Continue reading Polynomials – Exercise 8.5 – Class X

## Polynomials – Exercise 8.4 – Class X

Previous Exercise - Polynomials – Exercise 8.3 - Class X Polynomials – Exercise 8.4 In each of the following cases, use factor theorem to find whether g(x) is a factor of the polynomials p(x) or not. (i) p(x) = x3 – 3x2 + 6x – 20 ; g(x) = x – 2 (ii) p(x) =… Continue reading Polynomials – Exercise 8.4 – Class X