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Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Completion of Squares Method
If α, β are...
Question
If
α
,
β
are zeroes of the quadratic polynomial
a
x
2
+
b
x
+
c
then find the value of
α
2
−
β
2
.
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Solution
a
x
2
+
b
x
+
c
=
0
α
+
β
=
−
b
a
α
β
=
c
a
(
α
+
β
)
2
=
b
2
a
2
(
α
−
β
)
2
=
(
α
+
β
)
2
−
4
α
β
=
b
2
a
2
−
4
c
a
=
b
2
−
4
a
c
a
2
α
−
β
=
√
b
2
−
4
a
c
a
α
2
−
β
2
=
(
α
+
β
)
(
α
−
β
)
=
−
b
a
(
√
b
2
−
4
a
c
a
)
=
−
b
√
b
2
−
4
a
c
a
2
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Similar questions
Q.
If
α
and
β
are the zeros of the quadratic polynomial
f
(
x
)
=
a
x
2
+
b
x
+
c
, then evaluate:
α
2
β
+
α
β
2
Q.
If
α
,
β
are the zeros of the polynomial
f
(
x
)
=
a
x
2
+
b
x
+
c
then
1
α
2
+
1
β
2
Q.
Let
α
,
β
are the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
then find the value of
1
α
2
+
1
β
2
.
Q.
Let
α
,
β
be two roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
then find the value of
α
2
+
β
2
.
Q.
If α, β are the zeros of the polynomial ax
2
+ bx + c, then (α
2
+ β
2
) = ?
(a)
a
2
-
2
b
c
b
2
(b)
b
2
-
2
a
c
a
2
(c)
a
2
+
2
b
c
b
2
(d)
b
2
+
2
a
c
a
2
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Standard X Mathematics
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