Practice Sums for Quadratic Equation

Review :

Practice Examples 1  ,  Practice Examples 2

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Q.1

qtr2

A.  7

B.  8

C. -5

D. -2

E.  3

Solution;

( x+1)x = -2 (x-5) 

x2 + x = -2x + 10

x2 + x + 2x -10 = 0

x2 + 3x – 10 = 0

x2 + 5x – 2x – 10 = 0

x(x+5) -2(x+5) =0

(x+5) (x-2) = 0

Product of factors will be zero only when;

x+ 5 = 0 or x-2 = 0

x =-5 or x = 2

Maximum value of x = 2 and minimum value of x = -5

Difference between the two values is =2 – (- 5)

= 2 + 5

= 7

The answer is ‘A’.

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Q.2

QTR3

 A.  x > 7

 B.  x =5

 C.  -1 < x < 0

 D.  1<x<2

 E.  Cannot determine

Solution;

x(2x-1) = 2(5x+3)

2x2 – x = 10x+6

2x2 – x -10 x -6 = 0

2x2 – 11x – 6 = 0

2x2 – 12 x + x – 6 = 0

2x(x-6) + 1 (x-6) = 0

(x-6) (2x +1) = 0

(x-6) = 0 or (2x+1) = 0

x = 6 or x = -1/2

We are getting two values for ‘x’. If we look at the answer choices

  1. For A;    x > 7   , not possible for both values of ‘x’, this is not the answer.
  2. For B;   x =5 , Not satisfy the equation
  3. For C; -1 < x < 0 , Here the value of x is between – 1 and 0 which satisfy one of the value of x which is -1/2.
  4. For D; 1<x<2 ,  the value of x is between 1 and 2 which is not correct
  5. For E; Not valid statement

As per the answer choices given only ‘C’ satisfy the value -1/2 of x. The other value 6 is not given in the choices.

Hence, the correct answer is ‘C’.

                                                                              

  

Q.3

If  x2 – 8x -20 = 0

Quantity A                           Quantity B

Maximum value of x                        11

A.  If Quantity A is greater

B.  If Quantity B is greater

C.  If Quantity A and Quantity B are equal

D.  The relationship cannot be determined from given information

Solution;

x2 – 8x -20 = 0

x2 – 10x  + 2x – 20 = 0

x(x – 10) + 2 (x-10) = 0

(x-10) (x+2) = 0

(x-10) = 0 or (x +2) = 0

x = 10 or x = -2

The maximum value of x is 10 which is lesser than 11 so Quantity B is greater.

The correct answer is B.

                                                                                                 

Q.4

x2 + 1 = 26

Quantity A                           Quantity B

  x                                                  5

A.  If Quantity A is greater

B.  If Quantity B is greater

C.  If Quantity A and Quantity B are equal

D.  The relationship cannot be determined from given information

Solution;

x2 + 1 = 26

x2 + 1 – 26  = 0

x2 – 25  = 0

x2 – 5² = 0

(x – 5) (x + 5) = 0

x = 5 or x = -5

Let us compare the quantity A with B;

  1. When x = 5 Quantity A and quantity B are equal , the answer is ‘C’
  2. When x =-5 Quantity B is greater, the answer is ‘B’

Thus, the correct answer is ‘D’, as we cannot reach  any conclusion with the given data.

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