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Q2.    Represent the following situations in the form of quadratic equations :

(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.

Let the speed of the train be  km/h. The distance to be covered by the train is .  The time taken will be  If the speed had been  less, the time taken would be: . Now, according to question   Dividing by 3 on both the side  Hence, the speed of the train satisfies the quadratic equation

Q2.    Represent the following situations in the form of quadratic equations :

(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.

Let the age of Rohan be  years. Then his mother age will be:  years. After three years, Rohan's age will be  years and his mother age will be  years. Then according to question, The product of their ages 3 years from now will be:    Or    Hence, the age of Rohan satisfies the quadratic equation .

Q2.    Represent the following situations in the form of quadratic equations :

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

Given the product of two consecutive integers is  Let two consecutive integers be  and . Then, their product will be: Or . Hence, the two consecutive integers will satisfy this quadratic equation .

Q2.    Represent the following situations in the form of quadratic equations :

(i) The area of a rectangular plot is $528m^2$ . 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.

Given the area of a rectangular plot is . Let the breadth of the plot be . Then, the length of the plot will be: . Therefore the area will be:  which is equal to the given plot area . Hence, the length and breadth of the plot will satisfy the equation

Q1.    Check whether the following are quadratic equations :

(vii)    $(x+2)^3 = 2x(x^2 -1)$

L.H.S.  can be written as:   and R.H.S  can be written as: i.e.,  This equation is NOT of type: . Hence, the given equation is not a quadratic equation.

Q1.    Check whether the following are quadratic equations :

(vi)    $x^2 +3x +1 = (x-2)^2$

L.H.S.   and R.H.S  can be written as: i.e.,  This equation is NOT of type: . Here a=0, hence, the given equation is not a quadratic equation.

Q1.    Check whether the following are quadratic equations :

(iv)    $(x-3)(2x+1) = x(x+5)$

L.H.S.  can be written as: and R.H.S  can be written as: i.e.,  This equation is of type: . Hence, the given equation is a quadratic equation.

Q1.    Check whether the following are quadratic equations :

(v)    $(2x -1)(x-3) = (x+5)(x-1)$

L.H.S.  can be written as: and R.H.S  can be written as: i.e.,  This equation is of type: . Hence, the given equation is a quadratic equation.

Q1.    Check whether the following are quadratic equations :

(iii)    $(x-2)(x+1) = (x-1)(x+3)$

L.H.S.  can be written as: and R.H.S  can be written as: i.e.,  The equation is of the type: . Hence, the given equation is not a quadratic equation since a=0.

Q1.    Check whether the following are quadratic equations :

(i)    $(x+1)^2 = 2(x-3)$

We have L.H.S.  Therefore,  can be written as: i.e.,  Or  This equation is of type: . Hence, the given equation is a quadratic equation.

Q1.    Check whether the following are quadratic equations :

(ii)    $x^2 - 2x = (-2)(3-x)$

Given equation  can be written as: i.e.,  This equation is of type: . Hence, the given equation is a quadratic equation.
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