Solve quadratic given the roots

[Colin67]

My working so far




Now I am stuck!! I cannot eliminate so I can solve. I feel I am missing something fundamental.

Some guidance please would be appreciated

 

[Steven G]

You have 4 unknowns and 2 equations. So either you come up with 2 more equations and solve for c and d OR you solve for c and d in terms of alpha and beta? Which one do you think you should do?

 

[Deleted member 4993]

View attachment 23758


My working so far

View attachment 23759


Now I am stuck!! I cannot eliminate so I can solve. I feel I am missing something fundamental.

Some guidance please would be appreciated

α - ß = √(19/9 - 4*1/3) = √(7/9)

α + ß = 5/3

α = ? and ß = ?............................ continue................

 

[JeffM]

View attachment 23758


My working so far

View attachment 23759


Now I am stuck!! I cannot eliminate so I can solve. I feel I am missing something fundamental.

Some guidance please would be appreciated

What are the roots of the equation [MATH]3x^2 + 5x + 1[/MATH]?

So [MATH]\alpha = WHAT?[/MATH]
[MATH]\beta = WHAT?[/MATH]

 

[Colin67]

Thank you all, I was unsure how first part of question related to the second.

I found alpha and beta, substituted the values, c=-102, d=95

 

[Steven G]

The alpha and beta in the 2nd part are the same as the alpha and beta from the 1st part.

 

[Colin67]

Thank you all again