Question

Let s and t be the solutions of the quadratic 4x^2 + 9x - 6 = 0. Find

(s/t)+(t/s).

Please only give the numerical answer!

Answer 1

We have equation:


`4x^2 + 9x - 6 = 0`

When
`s` and
`t` are the solutions, from Vieta's formulas we know that:


`s+t=-(9)/(4)`

and:


`st=-(6)/(4)=-(3)/(2)`

So:


`(s)/(t)+(t)/(s)=(s^2)/(ts)+(t^2)/(ts)=(s^2+t^2)/(ts)=(s^2+t^2+2ts-2ts)/(ts)=((s+t)^2-2ts)/(ts)=\\\\\\= ((-(9)/(4))^2-2\cdot(-(3)/(2)))/(-(3)/(2))=((81)/(16)+3)/(-(3)/(2))=((81)/(16)+(48)/(16))/(-(3)/(2))=((129)/(16))/(-(3)/(2))=-(129\cdot2)/(16\cdot3)=\boxed{-(43)/(8)}`