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Need help solving this quadratic. How are the two equations related? Thanks.
The equation x^2 – 2x + 3 has roots α and β and the equation x^2 – 4x + p = 0 has roots k/α and k/β. Find the value k and of p. (Ans k = 6, p = 12)
Majors oops, sorry, repost again. Cut and paste from my Words and look what happened.
Anyway, here is my question again.
Need help solving this quadratic. How are the two equations related? Thanks.
The equation x^2 – 2x + 3 has roots α and β and the equation x^2 – 4x + p = 0 has roots
k/α and k/β. Find the value k and of p. (Ans k = 6, p = 12)
Originally posted by Jt061952:Majors oops, sorry, repost again. Cut and paste from my Words and look what happened.
Anyway, here is my question again.
Need help solving this quadratic. How are the two equations related? Thanks.
The equation x^2 – 2x + 3 has roots α and β and the equation x^2 – 4x + p = 0 has roots
k/α and k/β. Find the value k and of p. (Ans k = 6, p = 12)
(x-a)(x-b) = x^2 - (a+b)x + ab = x^2 - 2x + 3
= > a + b = 2 , ab = 3
= > (x-k/a)(x-k/b) = x^2 - ((a+b)k/ab)x + (k^2/ab) = x^2 - 4x + p
=x^2 - (2k/3)x + (k^2/3)
= > 2k/3 = 4 = > k = 6
= > p = k^2/3 = 36/3 = 12
Anything else wait for someone else to come, me going out liao.
Thanks Forbiddensinner for your swift response. jt
Hi,
Try this interesting question I obtained from Yahoo Answers:
For which real values of a do the equations
ax² + x + 1 = 0
and
x² + ax + 1 = 0
have at least one common root?
Thanks!
Cheers,
Wen Shih
all real values of a except 0?
-
Originally posted by SBS261P:all real values of a except 0?
Hi,
Not so straightforward. Let's apply Polya's problem-solving step 4 (check back the solution) to investigate further.
If we say a is any real value except 0, let's see what happens when we take a to be 1.
Both equations will become the same, i.e. x² + x + 1 = 0. However, no root satisfies the equation because its discriminant < 0.
Do try again :)
Cheers,
Wen Shih