Another complex number question (1 Viewer)

ashokkumar · Jan 2, 2010

Let H and K be the points representing the roots of x^2 + 2px + q = 0, where p and q are real and p^2 < q. Find the algebraic relation satisfied by p and q if angle HOK is a right angle.

jet · Jan 2, 2010

ashokkumar · Jan 2, 2010

wow thank you so much for everything Jetblack

jet · Jan 2, 2010

Haha, no worries, I'm happy to help

shaon0 · Jan 2, 2010

jetblack2007 said:
$\text{If } HOK \text{ is a right angle, that means that } HO \text{ is a 90 degree rotation meaning that } h = ik \text{ where } h \text{ and } k \text{ are the roots of the equation} \\ \text{Sum of roots } h + k = k + ik = k\left (1 + i \right ) = -2p \\ \text{Product of roots } hk = ik^2 = q \\ \text{Squaring the sum of roots: } k^2\left (1 + 2i - 1\right ) = 4p^2 \\ k^2 = \frac{2p^2}{i} \\ \therefore \text{ using the product of roots, } i\frac{2p^2}{i} = q \\ q = 2p^2$

Yeah. I got the same thing

Another complex number question (1 Viewer)

ashokkumar

Mr

jet

Banned

ashokkumar

Mr

jet

Banned

shaon0

...

Users Who Are Viewing This Thread (Users: 0, Guests: 1)