Maths Project Work [Autosaved]

7/31/2019 Maths Project Work [Autosaved]

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Quadratic Equation

If p(x) is a quadratic polynomial, then p(x) = 0 is called aquadratic equation.

The general form of quadratic equation is ax + bx + c = 0,

where a, b, c = R & a 0. Roots Of quadratic equations:Let p(x) = 0 be a quadratic

equation, then the zeroes of the polynomial p(x) are called the

roots of the equation p(x) = 0. Thus, x = is a roots of p(x)= 0 if and only if p() = 0.


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PolynomialAn Algebraic Expression with more than three terms is

called Polynomial. Zeroes of the polynomial: The values of variable X forwhich the value of polynomial will be zero is called zeroes of

the polynomial.

Solving a quadratic equation:

1.Factorisation Method.

a. Splitting Middle Term.

b. Formula 2.Completing square method.

3.Formula Method.


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f) Is there any real value of a for which the equation x + 2x +(a + 1) = 0 has real roots?

g) Write the condition to be satisfied for which equations ax + 2bx+ c = 0 and bx -2ac x + b = 0 have equal roots.

h) Find the discriminate of the quadratic equation 33x + 10x+ 3 = 0.

i) Write a quadratic polynomial, sum of zeroes is 23 and theirproduct is 2.

j) Show thatx = -3 is a sol. Of x + 6x + 9 = 0.


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3 marks questions

a) The perimeter of a rectangular field is 82m and its area is

400m. Find the breadth of the rectangle.b) The length of a hall is 5m more than its breadth. If the area of

the floor of the hall is 84m, what are the length and breadth ofthe hall ?

c) Two squares have sides x cm and (x + 4)cm. The sum of theirareas is 656cm. Find the sides of the squares.

d) The area of a right angled triangle is 165m. Determine its base

and altitude if the latter exceeds the former by 7m.e) Is it possible to design a rectangular mango grove whose length is

twice its breadth and the area is 800m ? If so, find its length

and breadth.


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f) Is it possible to design a rectangular park of perimeter 80m andarea 400m ? If so, find its length and breadth.

g) Sum of the areas of two squares is 640m. If the difference oftheir perimeters is 64m, find the sides of the two squares.

h)A takes 10 days less than the time taken by B to finish piece ofwork. If both A and B together can finish the work in 12 days, findthe time taken by B to finish the work.

i) If two pipes function simultaneously, a reservoir will be filled in 12hours. One pipe fills the reservoir 10 hours faster than the other.

How many hours will the second pipe take to fill the reservoir ?j) The side of a square exceeds the side of the another square by 4cm

and the sum of the areas of the two squares is 400 sq.cm. Find

the dimensions of the squares.


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4 marks questions

a) A person on tour hrs 360 for his expenses. If he extends tour for 4

days, he has to cut down his daily expenses by Rs 3. Find theoriginal duration of the tour.

b) A piece of clothe costs Rs 200. If the piece was 5m longer andeach meter of cloth costs Rs 2 less the cost of the piece would have

remained on changed. How long is the piece and what is theoriginal rate per meter ?

c) Rs 6500 were divided equally among a certain no. of persons.

Had there been 15 more persons, each would have got Rs 30 less.Find the original no. of persons.


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d)A shopkeeper buys a no. of books for Rs 80. If he had bought 4more books for the same amount, each book would have cost Rs 1less. How many books did he buys ?

e) If the price of a book is reduced by Rs 5, a person can buy 5 morebooks for Rs 300. Find the original list price of the book.

f)A factory kept increasing it is output by the same percentage every

year. Find the percentage if it is known that the output is doubledin the last two years.

g)A dealer sales a toy for Rs 24 and gains as much percent as the

cost price of the toy. Find the cost price of the toy.h) One-fourth of a herd of camels was seen in the forest. Twice the

square root of the herd had gone to mountains and the remaining15 camels were seen on the bank of a river. Find the total no. ofcamels.


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Multiple choice questions

1) If the equation x + 4x + k = 0 has real and distinct roots, then

a) k < 4 b) k > 4c) k 4 d) k 4

2) If the equation 9x + 6kx + 4 = 0 has equal roots, then the root are both equal to

a) 2/3 b) 3/2

c) 0 d) 3

3) A quadratic equation in the variable x is of the form ax + bx + c = 0, where a, b,c are real no. and

a) a = 0 b) a 0

c) a 0 d) a 0

4) If ax + bx + c = 0 has equal roots, then c =

a)b/ 2a b) b/ 2a

c)b/ 4a d) b/ 4a


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5) If the equation (a + b) x - 2 (ac + bd) x + c + d = 0 has equal roots, then

a) ab = cd b) ad = bc

c) ad = bc d) ab = cd

6) The quadratic equation 3x + 10x + 73 = 0 by factorization method. Then thetwo roots of the given equation are;-

a) x = -32 & x = 2 b) x = 2/3 & x = -1/3

c) x = -3 & x = -7/3 d) x = 5 & x = -4

7) If x = 1 is a common root of the equation ax + ax + 3 = 0 & x + x + b = 0,then ab =

a) 3 b) 3.5

c) 6 d) -3

8) If a & b can take values 1,2,3,4. Then the no. of the equations of the form ax + bx+ 1 = 0 having real roots is

a) 10 b) 7

c) 6 d) 12


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9) The positive value of k for which the equation x + kx + 64 = 0 & x - 8x + k =0 will both have real roots, is

a) 4 b) 8

c) 12 d) 16

10) If the equation ax + 2x + a = 0 has two distinct roots, if

a) a = 1 b) a = 0

c) a = 0, 1 d) a = -1, 0

Thank You !!

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Maths Project Work [Autosaved]