CBSE - Polynomials

1 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

2 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

3 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

4 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

5 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

6 Polynomials 

Find the remainder  when x⁴+x³-2x²+x+1 is divided by x-1

1) 1
2) 5 
3) 2 
4) 3 

7 Polynomials 

If zeroes of the quadratic polynomial x²+(a+1)x+b are 2 and -3 then find the value of a and b

1) 0, 6
2) 1, -6
3) 0, -6
4) -6, 0

8 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

9 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

10 Polynomials 

On dividing f(x) = x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and  – 2x + 4, respectively. Find g(x)..

1) x² – x + 1
2) x² + x + 1
3) x² – x – 1
4) x³ – x² +  x + 1