Quadratic Equations quiz

Which of the following is a quadratic equation?

The roots of x^2 - 3x - 10 = 0 are:

The discriminant of 2x^2 - 4x + 3 = 0 is:

The equation 3x^2 - 4sqrt(3)x + 4 = 0 has:

If x = 2 is a root of x^2 + kx - 10 = 0, the value of k is:

The value of k for which x^2 - 8x + k = 0 has equal roots is:

The roots of 2x^2 + x - 6 = 0 are:

Which equation has no real roots?

The sum of a number and its reciprocal is 10/3. The number is:

The maximum number of roots a quadratic equation can have is:

Find the roots of the quadratic equation x^2 - 3x - 10 = 0 by factorisation. (2 marks)

Find the roots of 3x^2 - 2sqrt(6)x + 2 = 0. (2 marks)

Find the discriminant of 2x^2 - 6x + 3 = 0 and state the nature of its roots. (2 marks)

Find the values of k for which 2x^2 + kx + 3 = 0 has two equal roots. (2 marks)

The product of two consecutive positive odd integers is 143. Form the quadratic equation for the smaller integer x. (2 marks)

Find two numbers whose sum is 27 and product is 182. (2 marks)

Is it possible to design a rectangular mango grove whose length is twice its breadth and whose area is 800 m^2? If so, find its length and breadth. (2 marks)

Solve x^2 + 4x + 5 = 0 using the discriminant and state your conclusion. (2 marks)

The sum of the squares of two consecutive odd positive integers is 290. Find the integers. (2 marks)

Rohan's mother is 26 years older than him. The product of their ages 3 years from now will be 360. Find Rohan's present age. (2 marks)

A cottage industry produces a certain number of pottery articles in a day. The cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article. (3 marks)

A motorboat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. (3 marks)

An express train takes 1 hour less than a passenger train to travel 132 km between Mysuru and Bengaluru, ignoring the time they stop at intermediate stations. If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains. (3 marks)

Sum of the areas of two squares is 468 m^2. If the difference of their perimeters is 24 m, find the sides of the two squares. (3 marks)

Two water taps together can fill a tank in 75/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. (3 marks)

Read the passage and answer the questions. John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. They want to find how many marbles they had to start with. (i) If John had x marbles, write the number of marbles Jivanti had, and the numbers each has after losing 5. (ii) Form the quadratic equation. (iii) Solve it to find the number of marbles each had at the start. (5 marks)

Read the passage and answer the questions. A community hall has a rectangular floor whose diagonal is 60 m more than the shorter side. The longer side is 30 m more than the shorter side. The committee wants to find the sides to plan the flooring. (i) Taking the shorter side as x m, write the longer side and the diagonal. (ii) Form the quadratic equation using Pythagoras theorem. (iii) Find the sides of the hall. (5 marks)

Read the passage and answer the questions. 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 product of her marks would have been 210. (i) Form the quadratic equation, taking her Mathematics marks as x. (ii) Solve the equation. (iii) Find her marks in the two subjects for each solution. (5 marks)

Read the passage and answer the questions. A school is planning a rectangular garden with a uniform path of width x m around a lawn of 20 m by 14 m. The total area of the lawn and path together must be 432 m^2. (i) Write the outer dimensions of the garden in terms of x. (ii) Form the quadratic equation in x and write it in standard form. (iii) Find the width of the path. (5 marks)

Read the passage and answer the questions. A ball is thrown upward and its height h (in metres) after t seconds is given by h = 20t - 5t^2. A student wants to know when the ball is at a height of 15 m. (i) Form the quadratic equation for h = 15. (ii) Solve it and interpret both roots. (iii) Using the discriminant, check whether the ball can ever reach a height of 25 m. (5 marks)

Explain the method of solving a quadratic equation by factorisation. Solve (i) 6x^2 - x - 2 = 0 (ii) 100x^2 - 20x + 1 = 0 and (iii) 2x^2 + x - 6 = 0 by this method. Draw a rough graph of y = 6x^2 - x - 2 showing where it cuts the x-axis. (6 marks)

State the quadratic formula. Use it to find the roots, if they exist, of (i) 2x^2 - 7x + 3 = 0 (ii) 2x^2 + x - 4 = 0 (iii) 4x^2 + 4sqrt(3)x + 3 = 0 (iv) 2x^2 + x + 4 = 0. In each case state the nature of the roots from the discriminant. (6 marks)

The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side, draw the figure, form the quadratic equation and find the lengths of the sides of the field. (6 marks)

A rectangular piece of cardboard 30 cm by 20 cm has equal squares of side x cm cut from its four corners, and the sides are folded up to make an open box. If the area of the base of the box is 336 cm^2, draw the net, form the quadratic equation, find x and the volume of the box. (6 marks)

Find the values of k for which each of the following has equal roots: (i) x^2 - 2(k + 1)x + k^2 = 0 (ii) kx^2 + 4x + 1 = 0. Then find the roots in each case and sketch the graph of the corresponding polynomial showing that it touches the x-axis. (6 marks)