**4. **QUADRATIC EQUATIONS

**MAX MARKS: – 15**

**TIME- 1 H **

**The train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.**[3]**A cottage industry produces a certain number of toys in a day. The cost of production of each toy was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs. 750. Find the number of toys produced on that day.**[3]**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. We would like to find out how many marbles they had to start with.**[3]**Find the value of k if the equation have two equal roots k x (x – 2) + 6 = 0.**[1]**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 of their ages in years was 48.**[3]**Find the nature of the roots of 3**[2]*x*^{2}– 4√3*x*+ 4 = 0. If the real roots exist, find them.