Finding the roots of a quadratic equation

[chwala]

Homework Statement

Kindly see the attached problem below

Relevant Equations

sum and products of roots of a quadratic equation

 

[chwala]

find my working on this below;

i would like you to check my working...is it correct?

 

[hutchphd]

After you find k (which you do correctly) just solve the equation explicitly as a check. You don't need my help.

 

[chwala]

i should be correct, checking with a previous example...

if i let $α=3$ and $β=1$, then $(x-3)(x-1)=x^2-4x+3$, $p=4$ and $q=3$
on forming the required quadratic with form $\frac {α}{β^2}$ and $\frac {β}{α^2}$,
we shall have,
$(x-\frac {1}{9}$)$(x-3)$=$x^2-\frac {28}{9}x$+$\frac {1}{3}$ which is in the required form...
similarly using the same thinking, and picking the roots $α=-3$ and $β=-3$ would yield the required form that i had shown in my working...
problem is can we let $α=β?$

 

[haruspex]

i should be correct, checking with a previous example...
View attachment 280707

if i let $∝=3$ and $β=1$,

Where does that combination come from? Did you mean α=β=3?
Btw, ∝ means "is proportional to". It is not a form of α (or in LaTeX, $\alpha$).

 

[chwala]

Where does that combination come from? Did you mean α=β=3?
Btw, ∝ means "is proportional to". It is not a form of α (or in LaTeX, α).

yeah, let me amend that...my eyes did not see that well..am getting old