if one root of the equation ax²+bx+c=0 is the cube of the other, prove that,(b²-2ac)²=ca(c+a)²
Answers
Answered by
2
Step-by-step explanation:
What would you like to ask?
10th
Maths
Quadratic Equations
Nature of Roots
If one root of the equation...
MATHS
avatar
Asked on December 30, 2019 by
Zilvi Sindhu
If one root of the equation ax
2
+bx+c=0;a,b,c∈R is cube of other, then
a+c
b
2
−2ac
is equal to
HARD
Share
Study later
ANSWER
Let the roots be α and α
3
∴α+α
3
=−
a
b
and α
4
=
a
c
⇒α
2
(1+α
2
)
2
=
a
2
b
2
⇒α
2
+2α
4
+α
6
=
a
2
b
2
⇒
a
c
+
a
2c
+
a
c
a
c
=
a
2
b
2
⇒
a
c
(1+
a
c
)=
a
2
b
2
−2ac
⇒
a
c
(
a
a+c
)
2
=
a
4
(b
2
−2ac)
2
⇒ac=(
a+c
b
2
−2ac
)
2
∴
a+c
b
2
−2ac
=±
ac
Similar questions