CHAPTER
–POLYNOMIAL LEVEL-I (each 1 marks)
1. The zeroes of the polynomial 2x2-3x-2
are
a. 1, 2 b.
-1/2,1 c. ½,-2 d.
-1/2,2
2. If a and b are zeroes
of the polynomial 2x2+7x-3, then the value of a2 +b2 is
a. 49/4 b.
37/4 c.
61/4 d.
61/2
3. If the polynomial 6x3+16x2+px
-5 is exactly divisible by 3x+ 5 , then the value of p is
a. -7 b.
-5 c.
5 d.
7
4. If 2 is a zero of the polynomials 3x2+ax-14 and
2x3+bx2+x-2, then the value of 2 - 2b is
a. -1 b.
5 c.
9 d.
-9
5. A quadratic polynomial whose product and sum of
zeroes are 1/3 and √2 respectively is
(a) 3x2 – x +3√ 2 (b) 3x2 +
x - 3√2 (c) 3x2 + 3√2x +1 (d) 3x2 – 3√2x
+1
LEVEL-II (each 2 marks)
1. If 1 is a zero of the polynomial p(x) = ax2 -3(a-1)
x -1, then find the value of a.
2. For what value of k, (-4) is zero of the
polynomial x2 – x –
(2k+2)?
3. Write a quadratic polynomial, the sum and
product of whose zeroes are 3 and -2.
4. Find the zeroes of the quadratic polynomial 2x2-9-3x
and verify the relationship between the zeroes and the coefficients.
5. Write the polynomial whose zeroes are 2 +√3 and
2 - √3.
LEVEL
– III (each 3 marks)
1. Find all the zeroes of the polynomial 2x3+x2-6x-3,
if two of its zeroes are -√3 and √3.
2. If the polynomial x4+2x3 +
8x2+12x+18 is divided by another polynomial x2+5, the
remainder comes out to be px+q. Find the value of p and
q.
3. If the polynomial 6x4+8x3+17x2+21x+7
is divided by another polynomial 3x2+4x+1, the remainder comes out
to be (ax+b), find a and
b.
4. If two zeroes of the polynomial f(x)= x3-4x2-3x+12
are √3 and -√3, then find its third zero.
5. If a, b are zeroes
of the polynomial x2-2x-15 then form a quadratic polynomial whose
zeroes are (2a) and (2b).
LEVEL
– IV (each 5 marks)
1. Find other zeroes of the polynomial
p(x)=2x4 +7x319x2-14x +30 if two of its
zeroes are √2 and -√2.
2. Divide 30x4 +11x3-82x2-12x-48
by (3x2 +2x-4) and verify the result by division algorithm.
3. If the polynomial 6x4 +8x3-5x2+ax+b
is exactly divisible by the polynomial 2x2-5, then find the value of
a and b.
4. Obtain all other zeroes of 3x4 -15x3+13x2+25x-30,
if two of its zeroes are and ±√5/3.
5. If a, b are zeroes
of the quadratic polynomial p(x)=kx2+4x+4 such that a2 +b2=24, find the
value of k.
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