Quadratic Equations — Practice

Question 1

Check whether (x - 2)(x + 1) = (x - 1)(x + 3) is a quadratic equation.

Accepted Answer

No, it is not quadratic

Question 2

Check whether x^3 - 4x^2 - x + 1 = (x - 2)^3 is a quadratic equation.

Accepted Answer

Yes, it is quadratic

Question 3

A train travels 480 km at a uniform speed. If the speed had been 8 km/h less, it would have taken 3 hours more for the same journey. Represent this as a quadratic equation.

Accepted Answer

x^2 - 8x - 1280 = 0, where x is the speed in km/h

Question 4

Find the roots of 2x^2 + x - 6 = 0 by factorisation.

Accepted Answer

x = 3/2 and x = -2

Question 5

Find the roots of root2 x^2 + 7x + 5 root2 = 0 by factorisation.

Accepted Answer

x = -root2 and x = -5/root2

Question 6

A cottage industry produces a number of articles in a day. On one day the cost of production of each article in rupees was 3 more than twice the number of articles produced. If the total cost that day was Rs 90, find the number of articles and the cost of each.

Accepted Answer

6 articles, each costing Rs 15

Question 7

Two trains leave a station at the same time, the first travelling west and the second north. The first travels 5 km/h faster than the second. If after two hours they are 50 km apart, find the average speed of each train.

Accepted Answer

20 km/h and 15 km/h

Question 8

A motor boat heads upstream a distance of 24 km on a river whose current runs at 3 km per hour. The trip up and back takes 6 hours. Assuming the boat keeps a constant speed, what was its speed in still water?

Accepted Answer

9 km/h

Question 9

Solve 1/(x + 4) - 1/(x - 7) = 11/30, where x is not -4 or 7.

Accepted Answer

x = 1 and x = 2

Question 10

The sum of the reciprocals of Rehman's age 3 years ago and his age 5 years from now is 1/3. Find his present age.

Accepted Answer

7 years

Question 11

Two water taps together can fill a tank in 9 and 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill it alone. Find the time each tap takes separately.

Accepted Answer

The smaller tap takes 25 hours and the larger 15 hours

Question 12

An object is thrown upwards with an initial velocity of 17 m/s from a building 12 m high. Its height above the ground after t seconds is S = 12 + 17t - 5t^2. Find the time it takes to touch the ground.

Accepted Answer

4 seconds

Question 13

If a polygon of n sides has n(n - 3)/2 diagonals, how many sides has a polygon with 65 diagonals? Is there a polygon with 50 diagonals?

Accepted Answer

13 sides; and no polygon has exactly 50 diagonals

Question 14

Find the nature of the roots of 2x^2 - 3x + 5 = 0.

Accepted Answer

No real roots exist

Question 15

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

Accepted Answer

k = 2 root6 or k = -2 root6

Question 16

Find the value of k for which kx(x - 2) + 6 = 0 has two equal roots, given k is not 0.

Accepted Answer

k = 6

Question 17

Is it possible to design a rectangular park of perimeter 80 m and area 400 square metres? If so, find its length and breadth, and comment.

Accepted Answer

Yes, and it is forced to be a square of side 20 m

Question 18

A piece of wire 8 m long is cut into two pieces, and each piece is bent into a square. Where should the cut be made if the sum of the areas of the two squares is to be 2 square metres?

Accepted Answer

At the midpoint, so both pieces are 4 m

Question 19

Vinay and Praveen working together can paint the exterior of a house in 6 days. Vinay by himself can complete the job in 5 days less than Praveen. How long will Vinay take alone?

Accepted Answer

10 days

Question 20

A two-digit number is such that the product of its digits is 8. When 18 is added to the number, the digits interchange their places. Find the number.

Accepted Answer

24

Question 21

Which of the following is NOT a quadratic equation? (a) x^2 - 6x - 4 = 0   (b) x^3 - 6x^2 + 2x - 1 = 0   (c) 7x = 2x^2   (d) 3y^2 = 192

Accepted Answer

(b) x^3 - 6x^2 + 2x - 1 = 0

Practice — Quadratic Equations

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