X MATHS POLYNOMIAL QUESTIONS SA I[2]

1.     On dividing the polynomial 3y³ – 4y² – 3y + 25 by a polynomial g(y), the quotient and remainder  were 3y + 5 and 5 respectively, find g (y).                                                                                                                                                                       

2.      The area of a rectangle remain the same if its length is increased by 7 cm and the breadth is decreased by 3 cm. The area remains unaffected if length is decreased by 7 cm and the breadth is increased by 5 cm. Find length and breadth.

3.       A no. consists of three digits whose sum is 17. The middle one exceeds the sum of other two by 1. If the digits are reversed, the no. is diminished by 396. Find the no.

4.     On dividing the polynomial 3x⁴ – 14x³+ 12x² + 6x + 5 by a polynomial g(x), the quotient and remainder were x² – 4x – 1 and 32x + 12 respectively, find g (x).                                                                     

5.       If the polynomial 3x³– 4x² – 17x + k is exactly divisible by 3x – 1 find the value of k..                         

6.       Solve for x and y :    2^x + 3^y = 17  and 2^{x + 2} – 3 ^y+1 = 5.

7.       If the polynomial 6x³+ 16x² + px – 5 is exactly divisible by 3x + 5, find the value of p.                          

8.   What real number should be subtracted from the polynomial 2x³+ 5x² – 14x + 10 so that the polynomial 2x – 3 divides it exactly?                  

9.       Find value of k so that the equations x + 2y = – 7, 2x + ky + 14 = 0 will represent coincident lines.

10.   Divide the polynomial (x⁴ + 1) by (x – 1) and verify the division algorithm.

11.   Find the polynomial of least degree which should be subtracted from the polynomial

x⁴ + 2x³– 4x² + 6x – 3 so that it is exactly divisible by x² – x + 1                                                                                       

12.   Give linear equations which is coincident with 2 x + 3y - 4 = 0 Find the value of K so that the pair of linear equations :          (3 K + 1) x + 3y – 2 = 0 

                                              (K² + 1) x + (k–2)y – 5 = 0 is inconsistent.

13.   Verify that – 2 is a zero of the polynomial 9x³+ 18x² – x – 2. Obtain all the zeroes .

14.   Find all the zeroes of 2x⁴ – 3x³– 3x² + 6x – 2, given that two of its zeroes are √2  and – √2 .  

15.   If two zeroes of the polynomial x⁴ – 6x³– 26x² + 138x – 35 are 2 ±√3  find other zeroes.      

16.   Find all the zeroes of the following polynomials :  (i) x³– 2x² – x + 2      (ii) 2x³  –  x² – 13x – 6.               

17.   If (x – 2) is a factor of x³+ ax² + bx + 16 and a – b = 6 find the values of a and b.       

        Ans:

1	[y2 – 3y + 4	6	FYS	11	x – 1	16	[(i) 1,2, -1 ;(ii) 3, -2 , -1/2 ]
2	Find Your self [FYS]	7	7	12	FYS	17	-2 , -8
3	FYS	8	7	13	[– 2 , 1/3 – 1/3
4	Q = 3x2 – 2x + 7	9	FYS	14	1, 1/2
5	6	10		15	7, -5