Hi,
May I please have your help in solving the problem below?
Thanks.
Show that the roots of the equation $\displaystyle x^2 - (a + d)x + (ad - b^2) = 0$ are real.
Yes Sir, I have. $\displaystyle b^2 - 4ac$ greater than or equal to zero;
$\displaystyle a = 1, b = a+d, c = ad - b^2$;
$\displaystyle b^2 = (a + d)^2 = a^2 + 2ad + d^2$;
$\displaystyle - 4ac = - 4(1)(ad - b^2) = - 4ad + 4b^2$;
However, how does one prove that $\displaystyle a^2 - 2ad + d^2 + 4b^2$ is greater than or equal to zero?