Applications of Second Degree Equations

Q.

In the Maths test two students, committed the following mistakes while solving a quadratic equation :
(i) One of them made a mistake in the constant term and got the roots as 2 and 4.
(ii) Another one committed an error in the coefficient of x and got the roots as 3 and 5.
But, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

1. $x^2+6x+15=0$

2. $x^2+15x-6=0$

3. $x^2-17x+6=0$

4. $x^2-6x+15=0$

Q.

A 2.6 m long rod leans against a wall, its foot 1 meters from the wall. When the foot is moved a little away from the wall, its upper end slides the same length down. How much farther is the foot moved?

Q.

The product of two consecutive positive integers is $306$. Find the integers.

1. 15 and 16

2. 16 and 17

3. 17 and 18

4. 18 and 19

Q.

Ganesh and Lokesh solved a quadratic equation. In solving it, Ganesh made a mistake in the constant term and got the roots as 6 and 7, while Lokesh made a mistake in the coefficient of x only and obtained the roots as 4 and 10. The correct roots of the equation are:

1. 8, 5

2. 8, -5

3. –8, –5

4. -8, 5

Q.

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/hr$ less, then it would have taken $3$ hours more to cover the same distance. The speed of the train is ___ kmph.

1. 48

2. 40

3. 45

4. 35

Q.

The sum of Arushi’s marks in Mathematics and Science is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Choose the correct options on the basis of this information.

1. Her marks in mathematics and science are 14 and 16

2. Her marks in mathematics and science are 12 and 18

3. Her marks in mathematics and science are 11 and 19

4. Her marks in mathematics and science are 13 and 17

Q.

A shopkeeper buys a number of books for ₹ 80. If he had bought 4 more books for the same amount, each book would have cost ₹ 1 less. He bought ___ books.

1. 12

2. 18

3. 14

4. 16

Q.

An aeroplane departed 30 minutes later than its scheduled time and in order to reach its destination which is 1500 km away on time, it had to increase its speed by 250 km/hr. Its original speed is ___ km/hr.

1. 800

2. 725

3. 700

4. 750

Q.

When each side of a square is reduced by 3 cm, the area becomes 49 sq cm. The side of the original square is ___ cm.

1. 5

2. 12

3. 10

4. 8

Q.

The sum of two numbers is 15. The sum of their reciprocals is $\frac{5}{18}$. Find the numbers.

1. 7 and 8

2. 9 and 6

3. 10 and 5

4. 11 and 4