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Byju's Answer
Standard X
Mathematics
Relationship Between Zeroes and Coefficients of a Quadratic Polynomial
If ‘α’ and ‘β...
Question
If ‘α’ and ‘β’ are the zeroes of the quadratic polynomial
p
(
x
)
=
x
2
+
7
x
+
5
,
then
(
α
−
β
)
2
equals
A
69
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B
29
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C
49
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D
9
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Solution
The correct option is
B
29
Given that α and β are zeroes of the quadratic polynomial
x
2
+
7
x
+
5.
∴ α + β = –7 and αβ = 5 …..(ii)
Now,
(
α
−
β
)
2
=
α
2
+
β
2
−
2
α
β
⇒
(
α
−
β
)
2
=
α
2
+
β
2
+
2
α
β
−
4
α
β
(Adding and subtracting 2αβ on RHS)
⇒
(
α
−
β
)
2
=
(
α
+
β
)
2
−
4
α
β
⇒
(
α
−
β
)
2
=
(
−
7
)
2
−
4
×
5
=
49
−
20
=
29
[Using (i)]
Hence, the correct answer is option (a).
Suggest Corrections
0
Similar questions
Q.
If ‘α’ and ‘β’ are the zeroes of the quadratic polynomial
p
(
x
)
=
x
2
+
7
x
+
5
,
then
(
α
−
β
)
2
equals
Q.
If
α
,
β
are the zeros of quadratic polynomial
f
(
x
)
=
x
2
−
p
x
+
q
, prove that
α
2
β
2
+
β
2
α
2
=
p
4
q
2
−
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2
q
+
2
Q.
If α and β are the zeros of the polynomial f(x) = x
2
+ px + q, from a polynomial whose zeros are (α + β)
2
and (α − β)
2
.