Show that the equation [tex]9x^2 - 17x - 85 = 0[/tex] provides solutions accurate to three significant figures.

There are two possible answers for [tex]x[/tex].

0\ \ \ \Rightarrow\ \ \ two\ real\ solution:\\\\x_1= \frac{\big{17- \sqrt{3349} }}{\big{2\cdot9}} =-2.27058584361...\approx-2.271\\\\x_2= \frac{\big{17+ \sqrt{3349} }}{\big{2\cdot9}} =4.1594747325...\approx4.159"> 9x^2-17x-85=0\\\\\Rightarrow\ \ \ \Delta=(-17)^2-4\cdot9\cdot(-85)=289+3060=3349\\\\\Delta>0\ \ \ \Rightarrow\ \ \ two\ real\ solution:\\\\x_1= \frac{\big{17- \sqrt{3349} }}{\big{2\cdot9}} =-2.27058584361...\approx-2.271\\\\x_2= \frac{\big{17+ \sqrt{3349} }}{\big{2\cdot9}} =4.1594747325...\approx4.159

Answered by kate200468 | 2024-06-10

The solutions to the equation 9 x 2 − 17 x − 85 = 0 are found using the quadratic formula. The two distinct real solutions are approximately − 2.27 and 4.16 when rounded to three significant figures. This shows that the equation provides accurate solutions as required.
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Answered by kate200468 | 2024-12-24