Scroll:Algebra >> Multiple Choice Questions: >> mcq (4180)


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For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

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Leave your answers in the simplest form or correct to two decimal places.



 

1)  

 The roots of the polynomial equation x2 +2x = 0 are 







(                    )




2)  

 The degree of the polynomial 4x-7x+ 6x + 1 is





 

(                    )




3)  

 .The coefficients of x2 and  x in 2x3 -3x- 2x + 3 are respectively






(                    )




4)  

  If the polynomial x3 –ax2+2x-a is divided (x-a), then remainder is

(1)⇒ a  
(2)⇒(a2)
(3) ⇒(a3)
(4) ⇒(-a)
 





(                    )




5)  

 The polynomial 3x-2 is a





 

(                    )




6)  

  If a polynomial p(x) is divided by (ax+b), then the remainder is





 

(                    )




7)  

 One of the factors of x-2x+2x -1 is






(                    )




8)  

 The zero of the polynomial 2x-5 is






(                    )




9)  

  The polynomial 4x2+2x-2 is a






(                    )




10)  

 The root of the polynomial equation 3x-1 = 0 is






(                    )




 

1)  

 The roots of the polynomial equation x2 +2x = 0 are 





Answer: 1



SOLUTION 1 :
Hint: [ [x2 +2x = 0   ⇒ x(x+2)=0   ⇒ x = 0 (or)  x + 2 = 0   ⇒ x=0  (or) x = -2   ⇒ x = 0,-2]
 
Ans =  x = 0, -2
 


2)  

 The degree of the polynomial 4x-7x+ 6x + 1 is





Answer: 2

 

SOLUTION 1 :
Hint: [The term having the highest degree is -7x3, The degree is 3]
 
Ans =3


3)  

 .The coefficients of x2 and  x in 2x3 -3x- 2x + 3 are respectively





Answer: 1


SOLUTION 1 :
Hint:[The co-efficient of x2 is- 3 and The co-efficient of x is -2]
 
Ans = -3,-2


4)  

  If the polynomial x3 –ax2+2x-a is divided (x-a), then remainder is

(1)⇒ a  
(2)⇒(a2)
(3) ⇒(a3)
(4) ⇒(-a)
 




Answer: 3


SOLUTION 1 :
Hint:[ [ p(x) = x3 – ax+ 2x- a ⇒ The zero of  x - a is a 
p(a) = a3-a(a)2+2(a)-a   ⇒  a3 - a3 + 2a - a = 2 ]
 
Ans = a


5)  

 The polynomial 3x-2 is a





Answer: 2

 

SOLUTION 1 :
Hint: [ The degree of 3x-2 is 1, It is a linear polynomial]
 
Ans = linear polynomial


6)  

  If a polynomial p(x) is divided by (ax+b), then the remainder is





Answer: 4

 

SOLUTION 1 :

Ans =  p(-ba)       



7)  

 One of the factors of x-2x+2x -1 is





Answer: 3


SOLUTION 1 :
Hint:[ (x-2x+ 2x -1 = x-x-x2 + x + x -1 = x2(x-1) – x(x-1) + 1(x-1) = (x-1) (x-x + 1) ]
 
Ans = x - 1


8)  

 The zero of the polynomial 2x-5 is





Answer: 2


SOLUTION 1 :
Hint: [ p(x) = 2x -5=2 ( x-52)   p(52) = 2(52-5 /2)=0. Hence x= 52is zero of p(x)
 
Ans = 52


9)  

  The polynomial 4x2+2x-2 is a





Answer: 2


SOLUTION 1 :
Hint: [ The degree of 4x2+2x-2 is 2, It is a quadratic polynomial]
 
Ans = quadratic polynomial


10)  

 The root of the polynomial equation 3x-1 = 0 is





Answer: 2


SOLUTION 1 :

Hint: [3x -1 = 0 ⇒ 3x = 1 ⇒ x = 13 ]

Ans = x = 13