CBSE - Polynomials

1 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

2 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

3 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
 

4 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

5 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

6 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

7 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

8 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

9 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

10 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