Class 10 Exam > Class 10 Notes > Exercise 4.3 - Quadratic Equations, Class 10, Maths
Exercise 4.3 - Quadratic Equations, Class 10, Maths PDF Download
Quadratic Equations
Exercise 3
Question: 1. The sum of the reciprocals of Rehman’s ages 3 years ago and 5 years from now is 1/3. Find his present age.
Question: 2. In a class test the sum of Shefali’s marks in Mathematics and English 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. Find her marks in two subjects.
Question: 3. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Question: 4. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
5. A train travels 360 kms at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
6. Two water taps together can fill a tank in 
hours. The tap of the larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
7. 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/h more than that of the passenger train, find the average speed of the two trains.
8. Sum of areas of two squares is 468 sqm. If the difference of their perimeters is 24 metres, find the sides of two squares.
FAQs on Exercise 4.3 - Quadratic Equations, Class 10, Maths
| 1. What is a quadratic equation? |  |
Ans. A quadratic equation is a polynomial equation of degree 2, which can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and 'x' is the variable.
| 2. How can I solve a quadratic equation? | |
Ans. Quadratic equations can be solved by various methods such as factoring, using the quadratic formula, completing the square, or graphing. The most commonly used method is the quadratic formula, which is x = (-b ± √(b^2 - 4ac))/(2a).
| 3. Can a quadratic equation have more than two solutions? | |
Ans. No, a quadratic equation can have at most two solutions. This is because a quadratic equation represents a parabola, which can intersect the x-axis at most twice.
| 4. What is the discriminant of a quadratic equation? | |
Ans. The discriminant of a quadratic equation is the expression b^2 - 4ac. It helps determine the nature of the solutions. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has two complex solutions.
| 5. Can a quadratic equation have no solutions? | |
Ans. Yes, a quadratic equation can have no real solutions if the discriminant is negative. However, it will still have two complex solutions.
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