# Quadratic Equations : Exercise 4.1 (Mathematics NCERT Class 10th)

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**Q.1 Check whether the following are quadratic equations :
**

**(i)**

**(ii)**

**(iii)**

**(iv)**

**(v)**

**(vi)**

**(vii)**

**(viii)**

**(i) We have**

*Sol.*Clearly, is a quadratic polynomial. So the given equation is a quadratic equation.

(ii) We have ,

Clearly, is a quadratic polynomial. SO, the given equation is a quadratic equation.

(iii) We have ,

Clearly, is linear polynomial So the given equation is not a quadratic equation.

(iv) We have,

Clearly, is a quadratic polynomial. So, the given equation is a quadratic equation.

(v) We have,

Clearly, is a quadratic polynomial. So, the given equation is a quadratic equation.

(vi) We have

Clearly, is a linear polynomial. So, the given equation is not a quadratic equation.

(vii) We have,

Clearly, being a polynomial of degree 3, is not a quadratic polynomial. So the given equation is not a quadratic equation.

(viii) We have,

Clearly, is a quadratic polynomial. So, the given equation is a quadratic equation.

**Q.2 Represent the following situation in the form of quadratic equations.
**

**(i) The area of a rectangular plot is . 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 year 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.**

* Sol. *(i) Let the length and breadth of the rectangular plot be 2x + 1 metres and x metres respectively. It is given that its area = .

Since

,

Which is the required quadratic equation satisfying the given conditions.

(ii) Let two consecutive integers be x and x + 1 such that their product = 306.

x (x + 1) = 306

Which is the required quadratic equation satisfying the given conditions.

(iii) Let Rohan 's present age be x years. Then,

His mother's age = (x + 26) years.

After 3 years, their respective ages are (x + 3) years and (x + 29) years. ... (1)

It is given that the product of, ages mentioned at (1) is 360

i.e. (x + 3)(x + 29) = 360

Therefore, the age of Rohan satisfies the quadratic equation .

(iv) Let u km/hr be the speed of the train.

Then, time taken to cover 480 km

Time taken to cover 480 km when the speed is decreased. by 8 km/hr

It is given that the time to cover 480 km is increased by 3 hours.

Therefore,

Therefore, the speed of the train satisfies the quadratic equation