Question

The equations 2x square + bx + c + 1 is equal to zero b, c belongs to cube and x square + 3 x minus 5 have common roots then value of b minus c is

Answer 1

Answer:

Suppose, α be the common root of the equations

x²+2x+3=0

and ax²+bx+c=0

Therefore α²+2α+3=0

Or, α²=-(2α+3) ····(1)

And aα²+bα+c=0

Or, aα²=-(bα+c)

Or, α²=-(bα+c)/a·····(2)

from (1) and (2) we get

-(bα+c)/a =-(2α+3)  

bα/a+c/a=2α+3

comparing both sides we have

b/a=2

Or b=2a

and c/a=3

Or, c=3a

Now a:b:c=a:2a:3a

Or, a:b:c=1:2:3