CBSE Class 10 Mathematics Quadratic Equations VBQs

Very Short Answer type Questions

Question. A train travels 360 km 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.
Answer : 40 km/h

Question. Find the roots of the quadratic equation : x - (1/4) = 3, x ≠ 0
Answer : 3 - √13 /2,3 + √13/2

Question. Sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares.
Answer : 18 m, 12 m

Question. Find the roots of the quadratic equation : 100 x² – 20x + 1 = 0.
Answer : 1/10, 1/10

Question. Find the nature of the roots of the quadratic equation 2x² – 3x + 5 = 0. If the real roots exist, find them.
Answer : Real roots do not exist

Question. Find the values of k for each of the quadratic equation kx (x – 2) + 6 = 0, so that they have two equal roots.
Answer : k = 6

Question. Represent the following situation in the form of quadratic equation : 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.
Answer : x² – 8x – 1280 = 0, where x (in km/h) is the speed of the train.

Question. 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 the two subjects.
Answer : Marks in mathematics = 12, marks in English = 18;
or, Marks in mathematics = 13, marks in English = 17

Question. Represent the following situation in the form of quadratic equation : The area of a rectangular plot is 528 m². 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.
Answer : 2x² + x – 528 = 0, where x is breadth (in metres) of the plot.

Question. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Answer : 5 cm and 12 cm

Question. 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.
Answer : 18, 12 or 18, –12

Question. Find the roots of the quadratic equation : 1/x+4 - 1/x-7 = 11/30. x ≠ -4, 7.
Answer : 1, 2

Question. An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.
Answer : Speed of the passenger train = 33 km/h, speed of express train = 44 km/h

Question. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Answer : 6 km/h.

Question. Find the roots of the quadratic equation: √2x² + 7 x + 5 √2 = 0.
Answer : - (5/√2), -√2