Problem: The difference of the roots of x2−7x−9=0x^{2}-7 x-9=0x2−7x−9=0 is:
Answer Choices:
A. +7+7+7 B. +72+\dfrac{7}{2}+27 C. +9+9+9 D. 2852 \sqrt{85}285 E. 85\sqrt{85}85 Solution:
The roots are (7±49+36)/2(7 \pm \sqrt{49+36}) / 2(7±49+36)/2 and their difference is 7+852−7−852=85\dfrac{7+\sqrt{85}}{2}-\dfrac{7-\sqrt{85}}{2}=\sqrt{85}27+85−27−85=85 or 7−852−7+852=−85\dfrac{7-\sqrt{85}}{2}-\dfrac{7+\sqrt{85}}{2}=-\sqrt{85}27−85−27+85=−85.
Of the given choices, (E) is correct.