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RD Chapter 2 Polynomials Ex 2.3 Solutions

Question - 1 : - Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in each of the following :

Answer - 1 : -


Question - 2 : - Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.
 

Answer - 2 : -


Question - 3 : - Obtain all zeros of the polynomial f(x) = 2x4 + x3 – 14x2 – 19x – 6, if two of its zeros are -2 and -1.

Answer - 3 : -


Question - 4 : - Obtain all zeros of f(x) = x3 +13x2 + 32x + 20, if one of itszeros is -2.

Answer - 4 : - f(x) = x3 +13x2 + 32x + 20
One zero = -2 or x = -2
x + 2 is a factor of f (x)
Now dividing f(x) by x + 2, we get

x + 1 = 0 => x = -1
and x + 10 = 0
=> x = -10
-1 and -10
Hence zeros are -10, -1, -2

Question - 5 : - Obtain all zeros of the polynomial f(x) = x4 – 3x3 –x2 + 9x – 6, if two of its zerosare – √3 and √3

Answer - 5 : -


Question - 6 : - Find all zeros of the polynomial f(x) = 2x4 – 2x3 –7x2 + 3x + 6, if its two zeros are √(3/2) and– √(3/2)

Answer - 6 : -


Question - 7 : - Find all the zeros of the polynomial x4 + x3 – 34x2 -4x+ 120, if two of its zeros are 2 and -2. [CBSE 2008]

Answer - 7 : -


Either x + 6 = 0, then x = -6
or x – 5 = 0, then x = 5
Hence other two zeros are -6, 5
and all zeros are 2, -2, -6, 5

Question - 8 : - Find all zeros of the polynomial 2x4 + 7x3 – 19x2 – 14x + 30, if two of its zeros are √2 and -√2

Answer - 8 : -


Question - 9 : - Find all the zeros of the polynomial 2x3 + x2 – 6x – 3, if two of its zeros are – √3 and √3. (CBSE 2009)

Answer - 9 : - Let f(x) = 2x3 +x2 – 6x – 3
and two zeros of f(x) are – √3 and √3

Question - 10 : - Find all the zeros of the polynomial x3 + 3x2 – 2x – 6, if two of its zeros are – √2 and √2 (CBSE2009)

Answer - 10 : -


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