1) If the polynomial f(x) = x4
– 25x + 10 is divided by another polynomial x2
-2x + k, the remainder comes out to be x + a, find k and a.
2) Find all the zeroes of the polynomial x4
+ 6x – 4, if two of its zeroes are √2 and -√2
3) If p and q are he zeroes of the quadratic polynomial f(x) = x2
– 2x + 3, find a polynomial whose roots are:
- p + 2, q + 2
- (p-1)/(p+1) , (q-1)/(q+1)
4) For what value of k, -7 is the zero of the polynomial 2x2 + 11x + (6k – 3)? Also find the other zero of the polynomial
What must be added to f(x) = 4x4
+ x – 1 so that the resulting polynomial is divisible by g(x) = x2
+ 2x -3?
6) Find k so that x2
+ 2x + k is a factor of 2x4
– 14 x2
+ 5x + 6. Also find all the zeroes of the two polynomials.
7) If the zeroes of the quadratic polynomial ax2
+ bx + c, c ≠ 0 are equal, then
(A) c and a have opposite signs
(B) c and b have opposite signs
(C) c and a have the same sign
(D) c and b have the same sign
8) Find the zeroes of 2x3
+ 17x – 6.
9) If (x - 2) and [x – ½ ] are the factors of the polynomials qx2
+ 5x + r prove that q = r
10) Find k so that the polynomial x2
+ 2x + k is a factor of polynomial 2x4
+ 5x + 6. Also, find all the zeroes of the two polynomials.
11) On dividing p(x) = x3
+ x + 2 by a polynomial q(x), the quotient and remainder were x – 2 and -2x + 4, respectively. Find g(x).
12) a, b, c are zeroes of cubic polynomial x3
+ qx – r. If a + b = 0 then show that 2q = r.
13) Find the remainder when x51
+51 is divided by (x+1).
14) a,b and c are zeroes of polynomial x3
+ qx + 2 such that a b + 1 = 0. Find the value of 2p + q + 5.
15) Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively
1) k = 5, a = -5
2) √2 , -√2, 2,1
4) -3, 3/2, -7
61x – 65
10) -3, -1/2, 1, 2
– x +1
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