Question 1:
Find the value of the polynomial 
at
at(i) x = 0 (ii) x = −1 (iii) x = 2
Ans.
(i) 
(ii)
(iii)
Question 3:
Verify whether the following are zeroes of the polynomial, indicated against them.
(i) 
(ii) 
(ii) (iii) p(x) = x2 − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2
(v) p(x) = x2 , x = 0 (vi) 
(vii) 
(viii) 
(viii) Ans.(i) If 
is a zero of given polynomial p(x) = 3x + 1, then 
should be 0.
is a zero of given polynomial p(x) = 3x + 1, then should be 0.
Therefore, is a zero of the given polynomial.
is a zero of the given polynomial.(ii) If 
is a zero of polynomial p(x) = 5x − π , then
should be 0.
is a zero of polynomial p(x) = 5x − π , thenshould be 0.
Therefore, is not a zero of the given polynomial.
is not a zero of the given polynomial.(iii) If x = 1 and x = −1 are zeroes of polynomial p(x) = x2 − 1, then p(1) and p(−1) should be 0.
Here, p(1) = (1)2 − 1 = 0, and
p(− 1) = (− 1)2 − 1 = 0
Hence, x = 1 and −1 are zeroes of the given polynomial.
(iv) If x = −1 and x = 2 are zeroes of polynomial p(x) = (x +1) (x − 2), then p(−1) and p(2)should be 0.
Here, p(−1) = (− 1 + 1) (− 1 − 2) = 0 (−3) = 0, and
p(2) = (2 + 1) (2 − 2 ) = 3 (0) = 0
Therefore, x = −1 and x = 2 are zeroes of the given polynomial.
(v) If x = 0 is a zero of polynomial p(x) = x2, then p(0) should be zero.
Here, p(0) = (0)2 = 0
Hence, x = 0 is a zero of the given polynomial.
(vi) If 
is a zero of polynomial p(x) = lx + m, then 
should be 0.
is a zero of polynomial p(x) = lx + m, then should be 0.Here, 
Therefore, 
is a zero of the given polynomial.
is a zero of the given polynomial.(vii) If 
and 
are zeroes of polynomial p(x) = 3x2 − 1, then
and are zeroes of polynomial p(x) = 3x2 − 1, then
Hence, is a zero of the given polynomial. However, is not a zero of the given polynomial.
is a zero of the given polynomial. However, is not a zero of the given polynomial.(viii) If 
is a zero of polynomial p(x) = 2x + 1, then 
should be 0.
is a zero of polynomial p(x) = 2x + 1, then should be 0.
Therefore, is not a zero of the given polynomial.
is not a zero of the given polynomial.Question 4:
Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5 (ii) p(x) = x − 5 (iii) p(x) = 2x + 5
(iv) p(x) = 3x − 2 (v) p(x) = 3x (vi) p(x) = ax, a ≠ 0
(vii) p(x) = cx + d, c ≠ 0, c, are real numbers.
Ans.
Zero of a polynomial is that value of the variable at which the value of the polynomial is obtained as 0.
(i) p(x) = x + 5
p(x) = 0
x + 5 = 0
x = − 5
Therefore, for x = −5, the value of the polynomial is 0 and hence, x = −5 is a zero of the given polynomial.
(ii) p(x) = x − 5
p(x) = 0
x − 5 = 0
x = 5
Therefore, for x = 5, the value of the polynomial is0 and hence, x = 5 is a zero of the given polynomial.
(iii) p(x) = 2x + 5
p(x) = 0
2x + 5 = 0
2x = − 5
Therefore, for, the value of the polynomial is 0 and hence, 
is a zero of the given polynomial.
, the value of the polynomial is 0 and hence, is a zero of the given polynomial.(iv) p(x) = 3x − 2
p(x) = 0
3x − 2 = 0
Therefore, for, the value of the polynomial is 0 and hence, is a zero of the given polynomial.
, the value of the polynomial is 0 and hence, is a zero of the given polynomial.(v) p(x) = 3x
p(x) = 0
3x = 0
x = 0
Therefore, for x = 0, the value of the polynomial is 0 and hence, x = 0 is a zero of the given polynomial.
(vi) p(x) = ax
p(x) = 0
ax = 0
x = 0
Therefore, for x = 0, the value of the polynomial is 0 and hence, x = 0 is a zero of the given polynomial.
(vii) p(x) = cx + d
p(x) = 0
cx+ d = 0
Therefore, for, the value of the polynomial is 0 and hence, is a zero of the given polynomial.
, the value of the polynomial is 0 and hence, is a zero of the given polynomial.