Directions:1-10) In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer.

1.

  1. x^2 – 26x + 168 = 0
  2. y^2 – 25y + 156 = 0

Ans:5

I. x^2 – 26x + 168 = 0

X^2 – 12x – 14x + 168 = 0

x (x – 12) – 14(x – 12) = 0

(x – 12) (x – 14) = 0

x = 12, 14

II. y^2 – 25y + 156 = 0

y^2 – 13y – 12y + 156 = 0

y(y – 13) – 12(y – 13) = 0

(y – 12) (y – 13) = 0

y = 12, 13

Hence, no relation can be established between x and y

2.

  1. 6x – 5y = -47
  2. 5x + 3y = 11

Ans:3
Equation (I) × 3 = 18x – 15y = -141

Equation (II) × 5 = 25x + 15y = 55

43x = -86

X = – 86/43 = 2

From II, we have,

5x + 3y = 11

3y = 11 – 5x

3y = 11 + 10

3y = 21

y = 7

Hence x < y

3.

I.2.3x – 20.01 = 0

II.2.9y – x = 0

Ans:1
I.2.3x – 20.01 = 0

X = 20.01 / 2.3 = 8.7

II.2.9y – x = 0

or, x = 2.9y

y = 8.7 /2.9 = 3

Hence x > y

4.

  1. x = √1764
  2. y^2 = 1764

Ans:2
I.x = 1764

x = 42

II.y^2 = 1764

y = + 42

Hence x ≥ y

5.

  1. x^2 – 13x + 42 = 0
  2. y^2 + y – 42 = 0

Ans:2
I.x^2 – 13x + 42 = 0

x^2 – 6x – 7x + 42 = 0

x(x – 6) – 7(x – 6) = 0

(x – 6) (x – 7) = 0

x = 6, 7

II.y^2 + y – 42 = 0

y^2 + 7y – 6x – 42 = 0

y(y + 7) – 6(y + 7) = 0

(y – 6)(y + 7) = 0

y = 6, – 7

Hence x ≥ y

6.

  1. 77X2 + 58X +8=0
  2. 56Y2+29Y +3=0

Ans:5

  1. 77X2 + 58X +8=0
  2. 56Y2+29Y +3=0

Sol: I. 77X2 + 58X +8=0

Or, 77X2+44X+14X+8=0

Or, 11X(7X+4)+2(7X+4)=0

Or, (11X+2)(7X+4)=0

Or, X= (-2)/11  ,  (-4)/7

II. 56Y2+29Y +3=0

Or, 56Y2+8Y+21Y+3=0

Or, 8Y(7Y+1)+3(7Y+1)=0

Or, (8Y+3)(7Y+1)=0

Or,  Y= (-3)/8  ,  (-1)/7

Hence, on relationship between x and y cannot be established

7.

  1. 43X2 – 90X +8=0
  2. 56Y2-36Y +4=0

Ans:5

  1. 43X2 – 90X +8=0
  2. 56Y2-36Y +4=0

Sol: I. 43X2 – 90X +8=0

Or, 43X2-86X-4X+8=0

Or, 43X(X-2)-4(X-2)=0

Or, (43X-4)(X-2)=0

Or, X= 2 , 4/43

II. 56Y2-36Y +4=0

Or, 56Y2-28Y-8Y+4=0

Or, 28Y(2Y-1)-4(2Y-1)=0

Or, (28Y-4)(2Y-1)=0

Or, Y = 4/28, 1/2

Hence, on relationship between x and y cannot be established.

8.

I. 34X2 – 140X +16=0

II. 24Y2-55Y+26=0

Ans:5

  1. 34X2 – 140X +16=0
  2. 24Y2-55Y+26=0

Sol: I. 34X2 – 140X +16=0

Or, 34X2-136X-4X+16=0

Or, 34X(X-4)-4(X-4)=0

Or, (34X-4)(X-4)=0

Or, X = 4, 4/34

II.24Y2-55Y+26=0

Or, 24Y2-16Y-39Y+26=0

Or, 8Y(3Y-2)-13(3Y-2)=0

Or, (8Y-13)(3Y-2)=0

Or, Y=2/3, 13/8

Hence, on relationship between x and y cannot be established.

9.

  1. 28X2 – 75X +17=0
  2. 36Y2-71Y +14=0

Ans:5

  1. 28X2 – 75X +17=0
  2. 36Y2-71Y +14=0

Sol: I. 28X2 – 75X +17=0

Or, 28X2-7X-68X+17=0

Or, 7X(4X-1)-17(4X-1)=0

Or, (7X-17)(4X-1)=0

Or, X= 17/7, 1/4

II. 36Y2-71Y +14=0

Or, 36Y2-8Y-63Y+14=0

Or, 4Y(9Y-2)-7(9Y-2)=0

Or, (4Y-7)(9Y-2)=0

Or, Y = 7/4  ,  2/9

Hence, on relationship between x and y cannot be established.

10.

  1. 19X2 – 84X +32=0
  2. 17Y2-75Y +28=0

Ans:5

  1. 19X2 – 84X +32=0
  2. 17Y2-75Y +28=0

Sol: I. 19X2 – 84X +32=0

Or, 19X2-76X-8X+32=0

Or, 19X(X-4)-8(X-4)=0

Or, (19X-8)(X-4)=0

Or, X= 4 , 8/19

II. 17Y2-75Y +28=0

Or, 17Y2– 68Y-7Y+28=0

Or, 17Y(Y-4)-7(Y-4)=0

Or, (17Y-7)(Y-4)=0

Or, Y= 4 ,7/17

Cannot be determined.

Pages: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

15 thoughts on “Quadratic Equation”

  2. sklep online

    Wow, fantastic weblog structure! How long have you ever been running a blog for?
    you make blogging glance easy. The full glance of your site
    is great, let alone the content material! You can see similar here sklep

  6. vorbelutr ioperbir

    magnificent post, very informative. I ponder why the opposite experts of this sector don’t notice this. You must continue your writing. I am sure, you have a huge readers’ base already!

  7. Anonymous

    Sir humari exam online hai to bank ki to hume waha rafh page provide kare gy jis hum numberical ki calculation kr sakhe ?

  8. Sapna

    Sir humari exam online hai to bank ki to hume waha rafh page provide kare gy jis hum numberical ki calculation kr sakhe ?

  9. Sapna

    Sir humari exam online hai to bank ki to hume waha rafh page provide kare gy jis hum numberical ki calculation kr sakhe ?

  11. tlovertonet

    I got what you mean , regards for posting.Woh I am lucky to find this website through google. “I would rather be a coward than brave because people hurt you when you are brave.” by E. M. Forster.

  12. ayuda TFM arquitectura

    A lot of thanks for all your valuable hard work on this website. Kim really loves conducting research and it’s obvious why. All of us learn all relating to the powerful means you give valuable information via the website and as well as recommend participation from website visitors on this article plus my princess is certainly becoming educated so much. Have fun with the rest of the year. You’re carrying out a brilliant job.

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top