**Notes**
**NCERT Solutions**
**Assignments**
**Revision Notes**
1) If the polynomial f(x) = x

^{4} -6x

^{3} + 16x

^{2} – 25x + 10 is divided by another polynomial x

^{2} -2x + k, the remainder comes out to be x + a, find k and a.
2) Find all the zeroes of the polynomial x

^{4} – 3x

^{3 }+ 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) = x

^{2} – 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 2x^{2} + 11x + (6k – 3)? Also find the other zero of the polynomial
5) What must be added to f(x) = 4x

^{4 }+ 2x

^{3} – 2x

^{2} + x – 1 so that the resulting polynomial is divisible by g(x) = x

^{2} + 2x -3?
6) Find k so that x

^{2} + 2x + k is a factor of 2x

^{4} + x

^{3} – 14 x

^{2} + 5x + 6. Also find all the zeroes of the two polynomials.
7) If the zeroes of the quadratic polynomial ax

^{2} + 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 2x

^{3} – 11x

^{2} + 17x – 6.
9) If (x - 2) and [x – ½ ] are the factors of the polynomials qx

^{2} + 5x + r prove that q = r
10) Find k so that the polynomial x

^{2} + 2x + k is a factor of polynomial 2x

^{4} + x

^{3} – 14x

^{2} + 5x + 6. Also, find all the zeroes of the two polynomials.
11) On dividing p(x) = x

^{3} – 3x

^{2} + 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 x

^{3} – 2x

^{2 }+ qx – r. If a + b = 0 then show that 2q = r.
13) Find the remainder when x

^{51} +51 is divided by (x+1).
14) a,b and c are zeroes of polynomial x

^{3 }+ px

^{2} + 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
Answer
1) k = 5, a = -5
2) √2 , -√2, 2,1
4)

-3, 3/2, -7
5) 61x – 65
10) -3, -1/2, 1, 2
11) x

^{2} – x +1
14) 0

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