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Birenkumar replied | 25/11/2016

Short method:
The difference between side1 and side 2 is Two and area is 195 so we can do multiplication of side 1 and side 2 up to getting area 195 base area of rectangle = side1×side2 (formula).
Side1 = 13 side2=15.

Daljit Kaur replied | 25/11/2016

13cm, 15cm

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A

Check whether the following equation is quadratic or not: square of x - 6 x - 4 = 0?

Tapas replied | 30/11/2016

This is a quadratic equation as highest power of x is 2.

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R

Determine whether the given value of x is a solution of the given equation or not: 2(square of x) - 6x + 3 = 0; x = 1/2 ?

Chandan replied | 22/11/2016

No, the given value of x is a solution of the given equation
since by putting the value of x in left hand side it is not making L.H.S= R.H.S.
So, x=1/2 is not the solution for the given quadratic equation.

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P

Determine whether the given value of x is a solution of the given equation or not: (2x + 3)(3x - 2) = 0; x = 2/3 ?

Ram Mohan replied | 21/11/2016

Yes.
The Given equation (2x+3) (3x-2)= 0 is True, ===> 3x-2 =0 ===> 3x=2 ===> x = 2/3.
Hence x = 2/3 is one solution, while, x= -3/2, is the other solution.

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U

Using factorization, find the roots of the quadratic equation: 9(square of x) - 16 = 0?

Tapas replied | 30/11/2016

9x^2 - 16 = 0
=> (3x)^2 = 4^2 =0
=> (3x + 4)(3x - 4)=0
so, 3x=4 --> x = 4/3
or, 3x=-4 --> x = -4/3
Answer: x = 4/3 or -4/3.

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P

Solve: 4(square of x) + 2x + 1 = 0?

Jeet replied | 02/12/2016

{-1+i(root3)}/4 and {-1-i(root3)}/4.

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A

Determine the value of p for which the given quadratic equation has real roots: p(square of x) + 4x + 1 = 0?

Tapas replied | 29/11/2016

The equation: px^2 + 4x + 1 = 0. The roots are real if the discriminant is zero or positive.
So, 4^2 - 4p >= 0 (>= means greater than or equal to).
=> p is smaller than or equal to 4.
Answer: p must be equal to 4 or smaller.

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A

The sum of a number and its reciprocal is 10/3, find the number?

Mamata replied | 24/11/2016

Let the number be a
a+(1/a)= 10/3
=> a^2+1)/a = 10/3
=> 3a^2+3-10a=0
=> 3a^2-10a+3=0
=> 3a^2-9a-a+3=0
=> 3a(a-3)-1(a-3)=0
=> (3a-1)(a-3)=0
=> a= 3 and a = 1/3

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P

A two digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their places. Find the number?

Sarvajeet replied | 23/11/2016

36.

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A

Find two consecutive odd natural numbers, the sum of whose squares is 202?

Chandan replied | 22/11/2016

x2+square of (x+2) =202.
Solving the quadratic equation we get
two odd natural numbers = 9,11 or -9,-11

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D

Determine two consecutive even positive integers, the sum of whose squares is 100?

Ram Mohan replied | 21/11/2016

Let the two consecutive even numbers be ' 2 a ' and ( 2 a + 2) where, a > 0 . Since the sum of their squares = 100; we get
4 a*a+ 4 ( a*a+2a+1) = 100==> 2a*a+2a+1 = 25==> 2 a*a + 2 a -24 =0 solving this,
we get a = 3 and a= -4. taking only +ve value of a=3, the required numbers are '6' and '8'.

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D

Dr. Rajani 03/11/2016 in  Quadratic Equations

There are three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154. What are the integers?

Shikha replied | 22/11/2016

Let first three consecutive numbers are x, x+1, x+2 . According to the question, x2+(x+1)(x+2)=154. Final answer is x=8. Hence numbers are 8,9,10.

Ankit replied | 23/11/2016

8, 9, 10.

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S

The hypotenuse of a grassy land in the shape of right triangle is 1 meter more than twice the shortest side. If the third side is 7 meters more than the shortest side, find the sides of the grassy land?

Tapas replied | 29/11/2016

Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition:
(2x +1)^2 = x^2 + (x + 7)^2.

Tapas replied | 29/11/2016

Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition:
(2x +1)^2 = x^2 + (x + 7)^2
=> 4x^2 + 4x + 1 = 2x^2 + 14x + 49
=> 2x^2 -10x - 48 = 0
=> x^2 - 5x - 24 = 0
=> x^2 - 8x + 3x -24 = 0
=> (x - 8)(x + 3) = 0
x = 8 or - 3. But the length of a side of a land cannot be negative....  more»
Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition:
(2x +1)^2 = x^2 + (x + 7)^2
=> 4x^2 + 4x + 1 = 2x^2 + 14x + 49
=> 2x^2 -10x - 48 = 0
=> x^2 - 5x - 24 = 0
=> x^2 - 8x + 3x -24 = 0
=> (x - 8)(x + 3) = 0
x = 8 or - 3. But the length of a side of a land cannot be negative.
So, x = 8m and the other sides are x + 7 = 15m, and (2x + 1) = 17m.
So, the sides of the land are 8m, 15m, and 17m. «less

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S

The difference of the squares of two numbers is 45. The squares of the smaller number is 4 times the larger number. Determine the numbers?

Sarvajeet replied | 23/11/2016

6, 9.

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B

The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages?

Suyash replied | 19/11/2016

Given,
F+S = 45
(F-5)×(S-5) = 124
On solving ,
F = 36 years
& S = 9 years

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K

A passenger train takes 2 hours less for a journey of 300 km, if its speed is increased by 5 km/hr from its usual speed. Find its usual speed?

Chandan replied | 22/11/2016

Let usual speed be x km/h
(300/x) - (300/(x+5)) = 2
solving it we get quadratic equation x2+5x-750=0
solving it get x=25 km/h.
Hence usual speed of train is 25 km/h.

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P

Check whether the following equation is quadratic or not: 16 (square of x) - 3 = (2x + 5) (5x - 3)?

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P

Using factorization, find the roots of the quadratic equation: [square of (x - 2)] - 25 = 0?

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R

Determine whether the given quadratic equation has root(s), if so find the root(s). [square of (y)] - 6y + 2 = 0?

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P

Solve: (x + 4)(x + 5) = 3(x + 1)(x + 2) + 2x?

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K

Divide 12 into two parts such that their product is 32?

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A

Divide 12 into two parts such that their product is 74?

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P

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 16/21, find the fraction?

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S

The product of Ramu’s age (in years) five years ago and his age (in years) nine years later is 15. Determine Ramu’s present age?

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A

The sum of two natural numbers is 8. Determine the numbers, if the sum of their reciprocals is 8/25?

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