if one root of the equation ax*x +bx+c=0 is three times the other then b*b - 4ac is
Answers
Step-by-step explanation:
ax
2
+bx+c=0
let one root beα
∴other root be 3α
sum=α+3α=4α=−
a
b
product=3α
2
=
a
c
α
2
=
3a
c
4α=−
a
b
∴α=−
4a
b
∴α
2
=
16a
2
b
2
or
3a
c
=
16a
2
b
2
ax
2
+bx+c=0
let one root beα
∴other root be 3α
sum=α+3α=4α=−
a
b
product=3α
2
=
a
c
α
2
=
3a
c
4α=−
a
b
∴α=−
4a
b
∴α
2
=
16a
2
b
2
or
3a
c
=
16a
2
b
2
16ac=3b
2ax
2
+bx+c=0
let one root beα
∴other root be 3α
sum=α+3α=4α=−
a
b
product=3α
2
=
a
c
α
2
=
3a
c
4α=−
a
b
∴α=−
4a
b
∴α
2
=
16a
2
b
2
or
3a
c
=
16a
2
b
2
16ac=3b ax
2
+bx+c=0
let one root beα
∴other root be 3α
sum=α+3α=4α=−
a
b
product=3α
2
=
a
c
α
2
=
3a
c
4α=−
a
b
∴α=−
4a
b
∴α
2
=
16a
2
b
2
or
3a
c
=
16a
2
b
2
16ac=3b
2ax
2
+bx+c=0
let one root beα
∴other root be 3α
sum=α+3α=4α=−
a
b
product=3α
2
=
a
c
α
2
=
3a
c
4α=−
a
b
∴α=−
4a
b
∴α
2
=
16a
2
b
2
or
3a
c
=
16a
2
b
2
16ac=3b
2
2
16ac=3b
2