Question

Solve the equation x^2 - (root3 + 1) x - bc = 0

Answer 1

I PROMISE U WILL FOLLOW YOU IF YOU AS BRAINLIST

THANKS FOR QUESTION

YOUR ANSWER IS

For quadratic equation ax

2

+bx+c=0

Sum of roots =−

a

b

Product of roots =

a

c

Let x

2

+ax+bc=0 have roots α and β:

α+β=−a......................(1)

αβ=bc...................(2)

Let x

2

+bx+ac=0 have roots α and γ:

α+γ=−b..................(3)

αγ=ac..................(4)

Subtracting (3) from (1) ,we get

β−γ=b−a..................(5)

Dividing (2) and (3)

γ

β

=

a

b

.................(6)

From (5) and (6)

β=b,γ=a

From (2)

α.b=bc⇒α=c

Now, equation having other roots is

x

2

−(β+γ)x+βγ=0

x

2

−(a+b)x+ab..................(7)

Since, β=b is the root of x

2

+ax+bc=0

⇒b

2

+ab+bc=0⇒a+b=−c

Putting this in (7)

we get x

2

+cx+ab=0