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Check whether the following are quadratic equations :
It is of the form
Hence it is a quadratic equation.
It is of the form
Hence it is a quadratic equation.
It is not of the form
Hence it is not a quadratic equation.
It is of the form
Hence it is a quadratic equation.
(v) It is of the form
Hence it is a quadratic equation.
(vi) It is not of the form
Hence it is not a quadratic equation.
(vii) It is not of the form
Hence it is not a quadratic equation.
(viii) It is of the form
Hence it is a quadratic equation.
Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 . 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 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/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
(i) If breadth =x,
length=2x+1,
area= length X breadth=
Simplifying
Factorising (2x +33)(x-16)=0,
x=
Rejecting the negative value, so x=16
Substituting, 2x+1=2x16+1=33
So breadth=16m, length=33m
(ii) Let the two consecutive numbers be x and (x+1)
(x-17)(x-18)=0,
so x=17, 18,consecutive integers are 17,18 as their product is 306
(iii) If Rohan's present age=x,
his mother's age=x+26,
3 years from now, their ages will be x+3 and and x+29,
So product=(x+3)(x+29)=360
(x+39)(x-7)=0. x= -39, x= 7
Rejecting negative value
x=7,x+26=7+26=33,So Rohan's present age=7 years
v) If the speed of train is xkm/hr.
Then time to travel 480km. is 480/x hour.
Speed X time= Distance
and with a speed of (x-8) km/hr,time=480/(x-8)hr.
So 480/(x-8)= (480/x)+3,
After simplifying we get
solving we get x=40,-32,
rejecting negative value
speed of the train=40km/hr.
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x "528(2x+1)x")
=&space;306 "x(x+1)= 306")
%5Cleft&space;(&space;%5Cfrac%7B480%7D%7Bx%7D&space;+3%5Cright&space;)=480 "(x-8)\left ( \frac{480}{x} +3\right )=480")
