24 solutions available
Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x – 2x = (- 2) (3-x) (iii) (x – 2) (x + 1) = (x – 1) (x + 3) (iv) (x –...
Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m2. The length of the plot (in...
Find the roots of the following quadratic equations by factorisation: (i) x2 -3x – 10 = 0 (ii) 2x2 + x – 6 = 0 (iii) √2x2 + 7x + 5√2 = 0 (iv) 2x2 – x...
Find two consecutive positive integers, the sum of whose squares is 365.
Solve the following situations mathematically: (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each and the product of the...
Find two numbers whose sum is 27 and product is 182.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each...
Find the roots of the following equations:
Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (i) 2x2 – 7x + 3 = 0 (ii) 2x2 + x – 4 = 0...
Find the roots of the quadratic equations by applying the quadratic formula. (i) 2x2 – 7x + 3 = 0 (ii) 2x2 – x + 4 = 0 (iii) 4x2 – 4√3x + 3 = 0 (iv)...
The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is \(\frac { 1 }{ 3 }\) Find his present age.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English,...
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the...
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of...
Two water taps together can fill a tank in 9\(\frac { 3 }{ 8 }\) hours. The tap of larger diameter takes 10 hours less than the smaller one to fill...
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bengaluru (without taking into consideration the time...
Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x² -3x + 5 = 0 (ii) 3x2 – 4√3x + 4 = 0...
Find the values of k for each of the following quadratic equations, so that they have two equal roots. (1) 2x2 + kx + 3 = 0 (2) kx (x – 2) + 6 = 0
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product...
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth. Solution:
