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Standard IX
Mathematics
Zeroes of a Polynomial
Zero of the p...
Question
Zero of the polynomial
p
(
x
)
where
p
(
x
)
=
a
x
,
a
≠
0
is :
A
1
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B
a
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C
0
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D
1
a
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Solution
The correct option is
C
0
Zeroes of the polynomial is the value of the variable for which the polynomial becomes
0
i.e.
p
(
x
)
=
0
.
Here,
p
(
x
)
=
a
x
.
Putting
p
(
x
)
=
0
, we get,
a
x
=
0
or,
x
=
0
(
∵
a
≠
0
)
So, option
C
is correct.
Suggest Corrections
2
Similar questions
Q.
Zero of the polynomial
p
(
x
)
where
p
(
x
)
=
a
x
,
a
≠
0
is :
Q.
Assertion :If p(x) is a polynomial of degree
≥
1 and ax+b is a factor of p(x) then we have
p
(
−
b
a
)
=
0
. Reason: If p(x) is a polynomial of degree
≥
1, then polynomial (x-a)(x-b) is a factor of p(x) if p(a)=0 and p(b)=0.
Q.
Find the zero of the polynomial in each of the following cases:
(i) p(x) = 3x - 2
(ii) p(x) = 3x
(iii) p(x) = ax, a
≠
0
(iv) p(x) = cx + d, c
≠
0, c, d are real numbers.
Q.
Verify that:
(i) 4 is a zero of the polynomial p(x) = x − 4.
(ii) −3 is a zero of the polynomial p(x) = x − 3.
(iii)
-
1
2
is a zero of the polynomial p(y) = 2y + 1.
(iv)
2
5
is a zero of the polynomial p(x) = 2 − 5x.
(v) 1 and 2 are the zeros of the polynomial p(x) = (x − 1)(x − 2).
(vi) 0 and 3 are the zeros of the polynomial p(x) = x
2
− 3x.
(vii) 2 and −3 are the zeros of the polynomial p(x) = x
2
+ x − 6.
Q.
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, d are real numbers.
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