Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Polynomials - 3
Total 25 marks, Time 55 mins.
1. On dividing a polynomial p(x) = x
3
- 3x
2
+ x + 2 by another polynomial g(x), the quotient and remainder were
(x-2) and (-2x+4). Find g(x). (3 marks)
2. Find the value of k such that the polynomial x
2
- (k+6)x + 2(2k -1) has sum of its zeroes equal to half of their
product. (2 marks)
3. Find the zeroes of the quadratic polynomial 8x
2
- 21 - 22x and verify the relationship between its zeroes and
the coefficients of the polynomial. (3 marks)
4. If the square of the difference of the zeroes of the polynomial f(x) = x
2
+ kx + 85 is equal to 144, evaluate the
value of k. (3 marks)
5. Divide 3x
3
+ x
2
+ 2x + 5 by 1 + 2x + x
2
, and verify the division algorithm. (4 marks)
6. Find the values of a and b so that x
4
+ x
3
+ 8x
2
+ ax + b is divisible by x
2
+ 1 (4 marks)
7. Find the zeroes of the polynomial f(x) = x
3
- 5x
2
- 16x + 80, if two of its zeroes are equal in magnitude but
opposite in sign. (3 marks)
8. A polynomial g(x) of degree 0 is added to the polynomial 2x
3
+ 5x
2
– 14x + 10 so that the resulting
polynomial is exactly divisible by 2x-3. Find g(x). (3 marks)
Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Answers:
1. g(x) = x^2 - x + 1
2. k=7
3. -3/4 and 7/2
4. k = +22 or -22
5. q(x) = 3x-5 and r(x) = 9x+10
For verification, just evaluate g(x)*q(x) + r(x) and verify that it is same as p(x) the dividend.
6. a = 1 and b = 7
7. 4, 5,-4
8. -7 must be added
