CBSE - Polynomials

1 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

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 

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

4 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

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 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 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

8 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

9 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

10 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