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RD Chapter 2 Polynomials Ex VSAQS Solutions

Question - 21 : - Give an example of polynomials f(x), g (x), q (x) and r (x) satisfying f(x) = g (x) . q (x) + r (x), where degree r (x) = 0.

Answer - 21 : -

f (x) = x3 + x2 + x + 4
g (x) = x + 1
q (x) = x2 + 1
r (x) = 3
is an example of f (x) = g (x) x q (x) + r (x)
where degree of r (x) is zero.

Question - 22 : - Write a quadratic polynomial, sum of whose zeros is 2√3 and their product is 2.

Answer - 22 : -

Sum of zeros = 2 √3
and product of zeros = 2
Quadratic polynomial will be f (x) = x2 – (sum of zeros) x + product of zeros
= x2 – 2 √3 x + 2

Question - 23 : - If fourth degree polynomial is divided by a quadratic polynomial, write the degree of the remainder.

Answer - 23 : -

Degree of the given polynomial = 4
and degree of divisor = 2
Degree of quotient will be 4 – 2 = 2
and degree of remainder will be less than 2 In other words equal to or less than one degree

Question - 24 : - If f(x) = x3 + x2 – ax + b is divisible by x2 – x, write the value of a and b.

Answer - 24 : -


Question - 25 : - If a – b, a and a + b are zeros of the polynomial f(x) = 2x3 – 6x2 + 5x – 7, write the value of a.

Answer - 25 : -


Question - 26 : - Write the coefficients of the polynomial p (z) = z5 – 2z2 + 4.

Answer - 26 : -

p (z) = z5 + oz4 + oz3 –2z2 + oz + 4
Coefficient of z5 = 1
Coefficient of z4 = 0
Coefficient of z3 = 0
Coefficient of z2 = – 2
Coefficient of z = 0
Constant = 4

Question - 27 : - Write the zeros of the polynomial x2 – x – 6. (C.B.S.E. 2008)

Answer - 27 : -


Question - 28 : - If (x + a) is a factor of 2x2 + 2ax + 5x + 10, find a. (C.B.S.E. 2008)

Answer - 28 : - x + a is a factor of

Question - 29 : - For what value of k, -4 is a zero of the polynomial x2 – x – (2k + 2) ? (CBSE 2009)

Answer - 29 : -


Question - 30 : - If 1 is a zero of the polynomial p (x) = ax2 – 3 (a – 1) x – 1, then find the value of a.

Answer - 30 : -


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