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.

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- Jul 16th 2013, 08:00 AMSeaniboyThe nature of the roots of a quadratic equation
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. - Jul 16th 2013, 08:20 AMProve ItRe: The nature of the roots of a quadratic equation
Have you tried checking the discriminant of this quadratic equation?

- Jul 16th 2013, 12:42 PMSeaniboyRe: The nature of the roots of a quadratic equation
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? - Jul 16th 2013, 12:47 PMMarkFLRe: The nature of the roots of a quadratic equation
Try factoring the first 3 terms as the square of a binomial...then you will have the sum of two squares...

- Jul 16th 2013, 01:10 PMPlatoRe: The nature of the roots of a quadratic equation
- Jul 17th 2013, 05:52 AMSeaniboyRe: The nature of the roots of a quadratic equation
Thanks Plato.

- Jul 17th 2013, 05:53 AMSeaniboyRe: The nature of the roots of a quadratic equation
Thanks Mark.