CBSE - Polynomials

1 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

2 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

3 Polynomials 

If one of the zeroes of the cubic polynomial ax³ + bx² + cx + d is zero, the product of then other two zeroes is

1) -c/a 
2) c/a 
3) 0 
4) -b/a 

4 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

5 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
 

6 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

7 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

8 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

9 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

10 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