CBSE - Polynomials

1 Polynomials 

If one of the zeroes of the quadratic polynomial (k-1)x² + kx + 1 is -3,then the value of k is 
1) -4/3
2) 4/3
3) 2/3
4) -2/3 

2 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

3 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
 

4 Polynomials 

If a and b are the zeroes of the polynomial  x²-11x +30, Find the value of a³ + b³

1) 134
2) 412
3) 256
4) 341

5 Polynomials 

If a and b are the zeros of the quadratic polynomial p(s) = 3s² – 6s + 4, find the value of 
 is

1) 4
2) 8
3) 6
4) 3

6 Polynomials 

If α  and  β are zeroes of the polynomial f(x)=x²+px+q then find the quadratic polynomial  having 1/α and 1/β as its zeroes

1) 2
2) 1
3) -1
4) 0

7 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

8 Polynomials 

If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 0 are equal, then
1) c and a have opposite signs
2) c and b have opposite signs
3) c and a have the same sign
4) c and b have the same sign

9 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
 

10 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