NCERT MATHS CLASS - X
Quadratic Equations
Quadratic Equations
Exercise 4.1
Question 1:
Check whether the following are quadratic equations:
Sol.
The given equation is in the form of ax2 + bx + c =0.
Hence it is a quadratic equation.
It is in the form of ax2 + bx + c =0.
Hence, it is a quadratic equation.
It’s not of the form of ax2 + bx + c =0.
Hence, the given equation is not a quadratic equation.
It is of the form ax2 + bx + c =0.
Hence, it is a quadratic equation.
It is of the form ax2 + bx + c =0.
Hence, it is a quadratic equation.
It is not of the form ax2 + bx + c =0.
Hence, it is not a quadratic equation.
Hence, it is not a quadratic equation.
Hence, it is a quadratic equation.
2.Represent the following situations in the form of quadratic equations.
(i) 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.
(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.
(i) Let the breadth of the plot be x m.
Hence, the length of the plot is (2x + 1) m.
Area of a rectangle = Length × Breadth
528 = x (2x + 1)
Or, 2x2 +x ─528 =0
(ii) Let the consecutive integers be x and x + 1.
It is given that their product is 306.
x(x+1) = 306
or, x2 +x ─ 306 =0
(iii) Let Rohan’s age be x.
Hence, his mother’s age = x + 26
3 years hence,
Rohan’s age = x + 3
Mother’s age = x + 26 + 3 = x + 29
It is given that the product of their ages after 3 years is 360.
(iv) Let the speed of train be x km/h.
Time taken to travel 480 km = 480/x hrs
In second condition, let the speed of train = (x─8)km/h
It is also given that the train will take 3 hours to cover the same distance.
Therefore, time taken to travel 480 km =
Speed × Time = Distance
