A child has a die whose six faces shows the letters as given below:
The die is thrown once. What is the probability of getting (i) A? (ii) D?
Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) \(2x^2 + kx + 3 = 0\) (ii) \(kx (x – 2) + 6 = 0\)
Solve the problems given in Example 1:-
(i) 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. Find out how many marbles they had to start with.
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) 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 out the number of toys produced on that day.
Find the roots of the following quadratic equations by factorisation: (i) \(x^2 – 3x – 10 = 0\)
(ii) \(2x^2 + x – 6 = 0\)
(iii) \(\sqrt2x^2+7x+5\sqrt2 = 0\)
(iv) \(2x^2 – x + \frac{1}8\)\( = 0\)
(v) \(100x^2 – 20x + 1 = 0\)
Represent the following situations in the form of quadratic equations.
(i) The area of a rectangular plot is 528 \(m^2\). The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) The product of two consecutive positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.
(iv) A 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. We need to find the speed of the train.
