Q. Solve : √ 2x^{2}+7x+5√2 = 0.
- Sol. Given,
- √ 2x2+7x+5√2 = 0.
- ⇒ √2x2+5x+2x+5√2=0
- ⇒ x(√2x+5)+√2(√2x+5)=0
- ⇒ (√2x+5)(x+√2)=0
- ⇒ x = −5/√2 and −√2.
- Ans.
Q. Solve: 3x^{2}+2√ 6x+2=0
Sol. Given, 3x^{2}+2√ 6x+2=0
Let the time taken by the first and second pipes to fill the pool simultaneously by t hours then, the third pipe also takes the same time to fill the pool.
(1/(x+5)+1/x)t=(1/(x-4))t
(1/(x+5)+1/x)=(1/(x-4))
⇒ (x – 10) (x + 2) = 0
But time cannot be negative. So, x = 10.
Hence, the time required to fill the pool by first pipe is 15 hrs. second pipe is 10 hrs and third pipe is 6 hrs. Ans.
Q. A train travels a distance of 480 km at uniform speed. If the speed had been 8 km/hr less, it would have taken 3 hours more to cover the same distance. Formulate the quadratic equation in terms of the speed of the train.
Q. The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.
- Ans. x^{2} + x – 306 = 0.
Q. 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 the product of the numbers of toys produced per day and 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. If x denotes the number of toys produced that day, form the quadratic equation to find x.
- Ans. x^{2} – 55x + 750 = 0.
Q. The height of a right-triangle is 7 cm less than the base. If the hypotenuse is 13 cm form the quadratic
- Ans. x^{2} – 7x – 60 = 0.
Q. Solve : 1/(x-2)+2/(x-1)=6/x, x≠0, 1, 2
- Ans. x = 3 and 4/ 3
Q. Solve : x +1/x=3, where x ≠0.
- Ans. x = (3±√ 5)/2
Q. Determine the roots of the equation
- 2x^{2} – 6x + 3 = 0.
- Ans. x = (3±√ 3)/2
Q. Find the value of k for which the equation kx(x – 2) + 6 = 0 has real and equal roots.
- Ans. k = 6.
Q. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than the passenger train, find the speeds of the two trains.
- Ans. The speed of the passenger train is 33 km/hr and the speed of the express train is 44 km / hr.
Q. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years hence is 1/3 Find his present age.
- Ans. 7 years.
Q. A pole has to be erected at a point on the boundary of a circular park of diameter 13 m in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 . If it is possible to do so, at what distances from the gates should the pole be erected?
- Ans. 5 metres and 12 metres.
- Ans. Breadth = 20 m and length = 40 m.
Q. Two water taps together take 9(3/8) hours to fill a tank. If the tap with the larger diameter takes 10 hours lesser than the tap with the smaller diameter, then find the time in which each tap can separately fill the tap.
- Ans. The smaller tap takes 25 hours to fill the tank and the larger one takes 15 hours to do so.
Q. In a class test, the sum of the marks obtained by Shefali in Mathematics and English was 30. Had she secured 2 more marks in Mathematics and 3 less in English then the product of the marks in both the tests would have been 210. Find the marks obtained by her in the two subjects separately.
- Ans. The marks obtained in Mathematics are either 13 or 12 and in English are 17 or 18.