# If one root of the equation ax*x +bx+c=0 is three times the other then b*b - 4ac is​

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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

497