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Byju's Answer
Standard X
Mathematics
Zeros of a Polynomial
1. Two zeroes...
Question
1.Two zeroes of the polynomial p(x)=x cube-4x square+x+6 are 2 and -1 of p(x)
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Solution
From given equation
a=1
b=-4
c=1
d=6
given two zeros -1 and 2
We know sum of zeros should be= -b/a
so z1+z2+z3= -(-4)/1
-1+2+z3=4
So z3=3
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Similar questions
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)
-
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(iv)
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(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
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(vii) 2 and −3 are the zeros of the polynomial p(x) = x
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Q.
Verify whether the following are zeroes of the polynomial, indicated against them.
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p
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5
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(iii)
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(iv) p(x) = (x +1) (x -2), x = - 1, 2
Q.
Question 3
Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x) = 3x + 1, x =
−
1
3
(ii)
p
(
x
)
=
5
x
−
π
,
x
=
4
5
(iii)
p
(
x
)
=
x
2
−
1
,
x
=
1
,
−
1
(iv) p(x) = (x +1) (x -2), x = - 1, 2
(v)
p
(
x
)
=
x
2
,
x
=
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(vi)
p
(
x
)
=
i
x
+
m
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=
−
m
i
(vii)
p
(
x
)
=
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x
2
−
1
,
x
=
−
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√
3
,
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p
(
x
)
=
2
x
+
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x
=
1
2
Q.
If
x
−
2
and
x
−
1
are the only zeroes of the polynomial
p
(
x
)
, which of the following is a zero of the polynomial
p
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x
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6
?
Q.
Question 3
Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x) = 3x + 1, x =
−
1
3
(ii)
p
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x
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=
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x
−
π
,
x
=
4
5
(iii)
p
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x
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x
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−
1
,
x
=
1
,
−
1
(iv) p(x) = (x +1) (x -2), x = - 1, 2
(v)
p
(
x
)
=
x
2
,
x
=
0
(vi)
p
(
x
)
=
i
x
+
m
,
x
=
−
m
i
(vii)
p
(
x
)
=
3
x
2
−
1
,
x
=
−
1
√
3
,
2
√
3
(viii)
p
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2
x
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2
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