1. Find the nature of the roots of the following quadratic equations. If real roots exist, find
them:
(i) 2x2– 3x + 5 = 0
(ii) 23 43 4 0 x x - +=
(iii) 2x2– 6x + 3 = 0
2. Find the values of k for each of the following quadratic equations, so that they have two
equal roots.
(i) 2x2 + kx + 3 = 0 (ii) kx (x – 2) + 6 = 0 (k ¹ 0)
3. 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.
4. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in
years was 48. Is the above situation possible? If so, determine their present ages.
5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m2
? If so, find its length and breadth. Comment on you answer.
OPTIONAL EXERCISE
[For extensive learing]
1. Some points are plotted on a plane such that any three of them are non collinear. Each
point is joined with all remaining points by line segments. Find the number of points if the
number of line segments are 10.
2. A two digit number is such that the product of its digits is 8. When 18 is added to the
number they interchange their places. Determine the number.
3. A piece of wire 8 m. in length is cut into two pieces, and each piece is bent into a square.
Where should the cut in the wire be made if the sum of the areas of these squares is to be 2m2
Hint :[x+y=8,(x/4)2+(y/4)2=2==>(x/4)2+(8-x/4)2=2]
4.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 it take Vinay to
complete the job.
5. Show that the sum of roots of a quadratic equation ax2+ bx + c =0 (a≠0) is (-b/a)