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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 2 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 1 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 4 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 2 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 1 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 2 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 2 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 3 Solution : -. |
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
A. | Option 1 |
B. | Option 2 |
C. | Option 3 |
D. | Option 4 |
Option: 2 Solution : -. |