Page 28 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

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12. If the roots of the equation x +2cx+ab=0 are real and unequal,
prove that the equation x -2(a+b)+a +b +2c =0 has no real roots.
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13. A chessboard contains 64 equal squares, and the area of each
square

is 6.25cm . A border round the board is 2cm wide. Find the length
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of

the side of the chessboard.

14. A industry produces a certain number of pottery articles in a day.

It was observed on a particular day that the cost of production of

each article(in rupees) was more than twice the number of articles

produced on that day. If the total cost of production on that day

was Rs 90, find the number of articles produced and the cost of

each article.

15. Seven years ago, Vaarun's age was five times the square of Swati's

age. Three years hence Swati's age will be two-fifth of Vaarun's age.

Find their present ages.

16. A super express train takes 1 hour less than a passenger train to

travel 132km between Asansol and Haldia(without taking into

consideration the time they stop at intermediate station). If the

average speed of the super express train is 11km/h more than that

of the passenger train, find average speed of the two trains.

17. Divide 16 into two parts such that twice the square of the larger

part exceeds the square of the smaller part by 164.

18. A plane left 30 minutes later than the scheduled time in order to

reach its destination 1500km away in time, it has to increase its

speed by 250km/hr from its usual speed. Find its usual speed?

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