Math Homework Help

[christina.staikos27]

Please help!

 

I cannot figure out this question:

Let a and b denote the roots of the quadratic equation x² - kx + (k-1) = 0

(a) Express a and b in terms of k

(b) Given that a² +b² =17, find the possible values of k.

[kw0573]

This makes use of viete's theorem, which is HL only. The theorem, applied to a quadratic, says roots add to negative of the coefficient of x (-B) in the form x^2 + Bx + C, and multiply to C.

In other words, a + b = -(-k)=k, ab = k-1

a^2 + b^2 = (a+b)^2-2ab = 17 = k^2 - 2(k-1)

k^2-2k-15=0, (k-5)(k+3) = 0, k=-3, 5

Or what I mean is that the way the question is set up it asks you to plug -k and k-1 into quadratic formula to essentially prove viete's theorem. I admit it's hard to do if you have no exposure to viete's theorem.

Edited February 1, 2017 by kw0573