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D Divya Prakash Singh
(i)  The general form of a quadratic equation is : , where a, b, and c are arbitrary constants. Hence on comparing the given equation with the general form, we get And the quadratic formula for finding the roots is: Substituting the values in the quadratic formula, we obtain Therefore, the real roots are:    (ii)  The general form of a quadratic equation is : , where a, b, and c are...

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D Divya Prakash Singh
Given equation:  On dividing both sides of the equation by 2, we obtain Adding and subtracting   in the equation, we get Here the real roots do not exist (in the higher studies we will study how to find the root of such equations).  

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D Divya Prakash Singh
Given equation:  On dividing both sides of the equation by 4, we obtain Adding and subtracting    in the equation, we get Hence there are the same roots and equal:

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D Divya Prakash Singh
Given equation:  On dividing both sides of the equation by 2, we obtain Adding and subtracting    in the equation, we get    

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D Divya Prakash Singh
Let the number of articles produced in a day  The cost of production of each articles will be  Given the total production on that day was . Hence we have the equation; But, x cannot be negative as it is the number of articles. Therefore,  and the cost of each article  Hence, the number of articles is 6 and the cost of each article is Rs.15.    

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D Divya Prakash Singh
Let the length of the base of the triangle be . Then, the altitude length will be: . Given if hypotenuse is . Applying the Pythagoras theorem; we get So,    Or   But, the length of the base cannot be negative.  Hence the base length will be . Therefore, we have Altitude length   and  Base length       

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D Divya Prakash Singh
Let the two consecutive integers be  Then the sum of squares is 365. . Hence, the two consecutive integers are .    

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D Divya Prakash Singh
Let two numbers be x and y. Then, their sum will be equal to 27 and the product equals 182.                                         ...............................(1)                                            .................................(2) From equation (2) we have:  Then putting the value of y in equation (1), we get Solving this equation: Hence, the two required numbers are .        

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D Divya Prakash Singh
From Example 1 we get: Equations: (i)  Solving by factorization method:  Given the quadratic equation:  Factorization gives,  Hence, the roots of the given quadratic equation are . Therefore, John and Jivanti have 36 and 9 marbles respectively in the beginning. (ii)  Solving by factorization method:  Given the quadratic equation:  Factorization gives,  Hence, the roots of the given...

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D Divya Prakash Singh
Given the quadratic equation:  Solving the quadratic equations, we get Factorisation gives,  Hence, the roots of the given quadratic equation are  .

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D Divya Prakash Singh
Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are  .

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D Divya Prakash Singh
Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are  .

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D Divya Prakash Singh
Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are  .

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D Divya Prakash Singh
Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are .

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D Divya Prakash Singh
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  

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D Divya Prakash Singh
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 .

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D Divya Prakash Singh
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 .

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D Divya Prakash Singh
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   

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D Divya Prakash Singh
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.
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