(ii)
x² - ax + b
(x-p)(x-2)(x-)
Answers
Answer:
Step-by-step explanation:
f α & β are the roots of
$$px2+qx+r=0$$
then
$$αβ=−qp$$
αβ=rp
_______________________________
x2+ax+b=0−−−(1)
x2+cx+d=0−−−(2)
let the common root be α
for eqn(1)
α+α=−a
⇒α=−a2
& α2=b
for the eqn(2) let the second root be β
then
α+β=−c
αβ=d
⇒β=dα
∴α+dα=−c
α2+d=α(−c)
b+d=(−a2)(−c)
∴2(b+d)=ac as reqd.
Answer:
Step-by-step explanation:
note:
for this problem we will use the property of the sum and product of roots of a quadratic
that is
if
α
&
β
are the roots of
p
x
2
+
q
x
+
r
=
0
then
α
β
=
−
q
p
α
β
=
r
p
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_
x
2
+
a
x
+
b
=
0
−
−
−
(
1
)
x
2
+
c
x
+
d
=
0
−
−
−
(
2
)
let the common root be
α
for eqn
(
1
)
α
+
α
=
−
a
⇒
α
=
−
a
2
&
α
2
=
b
for the eqn
(
2
)
let the second root be
β
then
α
+
β
=
−
c
α
β
=
d
⇒
β
=
d
α
∴
α
+
d
α
=
−
c
α
2
+
d
=
α
(
−
c
)
b
+
d
=
(
−
a
2
)
(
−
c
)
∴
2
(
b
+
d
)
=
a
c
as reqd.