CBSE - Polynomials

1 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

2 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 

3 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

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 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 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 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

10 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