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Byju's Answer
Standard XII
Mathematics
Relations between Roots and Coefficients : Higher Order Equations
if alpha and ...
Question
if alpha and beta are the zeroes of the polynomial x^2 - (k+6)x+2(2k-1) such that alpha + beta = 1/2 alpha* beta find the value of k
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Solution
Let
p
x
=
x
2
-
k
+
6
x
+
2
2
k
-
1
Now
,
α
and
β
are
the
zeroes
of
p
x
,
then
α
+
β
=
-
coefficient
of
x
coefficient
of
x
2
=
k
+
6
1
=
k
+
6
αβ
=
2
2
k
-
1
1
=
4
k
-
2
Now
,
α
+
β
=
1
2
αβ
⇒
k
+
6
=
1
2
4
k
-
2
⇒
k
+
6
=
2
k
-
1
⇒
k
-
2
k
=
-
1
-
6
⇒
-
k
=
-
7
⇒
k
=
7
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2
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