# 10th cbse maths solution for exercise 4.1

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## 10th cbse maths solution for exercise 4.1

(1) Check whether the following are quadratic equations:

(i) (x + 1)²= 2 (x – 3)

(ii) x² - 2 x = (-2) (3 - x)

(iii) (x - 2) (x + 1) = (x - 1) (x + 3)

(iv) (x - 3) (2x + 1) = x (x + 5)

(v) (2 x - 1) (x - 3) = (x + 5) (x - 1)

(vi) x² + 3 x + 1 = (x - 2)²

(vii) (x + 2)³ = 2 x (x² - 1)

(vii) x³ - 4 x² - x + 1 = (x - 2)³

(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 meters) 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/hr less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

(i) (x + 1)² = 2 (x – 3)

Solution:

To check whether the given equation
is quadratic equation, it must be in the form of ax² + bx + c = 0

(x + 1)² = 2 (x – 3) can be rewritten as

x²+ 2 x + 1 = 2 x – 6

x² + 2 x – 2 x + 1 + 6 = 0

x² + 7 = 0

This exactly matches the general form of quadratic equation

Therefore the given equation is quadratic equation

(ii) x² – 2 x = (-2) (3 – x)

Solution:

x² – 2 x = - 6 + 2
x

x² – 2 x – 2 x + 6
= 0

x² – 4 x + 6 = 0

This exactly matches the general form of quadratic equation

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