Polynomials Foundation CUET CBSE questions

CBSE - Polynomials

 

Polynomials 

If α, β are the zeros of the polynomial f(x) = x2 + x + 1, then =

1) 1
2) -1
3) 0
4) None of these

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 2

Solution :

-.

 

Polynomials 

Given that two of the zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0, the third zero is
1) -b /a
2) b /a
3) c /a
4) -d /a

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 1

Solution :

-.

 

Polynomials 

If f(x) = ax2 + bx + c has no real zeros and a + b + c < 0, then

1) c = 0
2) c > 0
3) c < 0
4) None of these

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 4

Solution :

-.

 

Polynomials 

If α, β are the zeros of polynomial f(x) = x2 – p (x + 1) – c, then (α + 1) (β + 1) =

(a) c – 1
(b) 1 – c
(c) c
(d) 1 + c

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 2

Solution :

-.

 

Polynomials 

If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of other two zeroes is

1) b – a + 1
2) b – a – 1
3) a – b + 1
4) a – b – 1

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 1

Solution :

-.

 

Polynomials 

The zeroes of the quadratic polynomial x2 + 99x + 127 are

1) both positive
2) both negative
3) both equal
4) one positive and one negative

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 2

Solution :

-.

 

Polynomials 

p(x) = x4 -6x3 +16x2 -25x +10
     q(x) = x2-2x+k
It is given
p(x) = r(x) q(x) + (x+a)
Find the value of k and a

1) 2,-2
2) 5 ,-5
3) 7,3
4) 3,-1
 

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 2

Solution :

-.

 

Polynomials 

If the polynomial  x3 + 2x2 - αx - 12   is divided by   (x - 4)  the remainder is 52. Find the value of 

1) 11 / 2
2) - 5
3) 8
4)  - 8

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 3

Solution :

-.

 

Polynomials 

If α and β are the zeroes of the polynomial f(x) = x2 – 5x + k such that α – β = 1, then value of k is: 

(1) 8 
(2) 6
(3) 13 / 2
(4) 4

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 2

Solution :

-.

 

Polynomials 

If a and b are the roots (zeros) of the polynomial f(x) = x2 – 3x + k such that α – β= 1, find the value of k.

1) 1
2) 4
3) 2
4) 5

 

A. Option 1
B. Option 2
C. Option 3
D. Option 4
 
 

Option: 3

Solution :

-.

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