roots and co-efficients of polynomial equations (1 Viewer)

[Schniz]

have a couple of questions....

*Solve the equation x^3 - 14x^2 + 56x - 64 = 0 if the roots are in geometric progression.

*Given that the equation x^3 - 7x^2 + 16x + k = 0 has two equal and integral roots find the value of k.

 

[Schniz]

thanks ;-)

 

[Forbidden.]

Is this in the preliminary course or HSC course ?

 

[Slidey]

Keep in mind, however, that the topics which are considered part of the preliminary course by the syllabus can only be assessed up to a certain amount in exams. It's something like 30%.

But, as stated, maths is holistic. You don't know which topics will be part of that 30%, and even if you did, you need to know everything, anyway, since the HSC course is built on it.

 

[Riviet]

*Solve the equation x^3 - 14x^2 + 56x - 64 = 0 if the roots are in geometric progression.

Instead of having the roots as a, ar and ar², you could instead try a/r, a and ar. I believe this results in slightly easier algebra, particularly with the sum of the roots since the r's cancel each other out.