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Chapter 2: Problem 46

Solve each quadratic equation using the quadratic formula. Express solutions in standard form. $$x^{2}-2 x+17=0$$

Short Answer

Expert verified
The solutions to the quadratic equation \(x^{2}-2 x+17=0\) are \(x = 1+8i\) and \(x = 1-8i\).

Step by step solution

01

Identify coefficients

In the given quadratic equation \(x^{2}-2 x+17=0\), the coefficients are \(a = 1\), \(b = -2\), and \(c = 17\).
02

Compute the discriminant

The discriminant of a quadratic equation \(ax^{2}+bx+c = 0\) is given by \(b^{2} - 4ac\). In this case, the discriminant is \((-2)^{2} - 4*1*17 = 4 - 68 = -64\).
03

Apply the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4 a c}}{2 a}\). Substitute \(a=1, b=-2, c=17\) into the formula to find the roots of the equation: \(x = \frac{2 \pm \sqrt{-64}}{2} = 1 \pm 8i\), where \(i = \sqrt{-1}\).

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Most popular questions from this chapter

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The rational function $$f(x)=\frac{27,725(x-14)}{x^{2}+9}-5 x$$ models the number of arrests, \(f(x),\) per 100,000 drivers, for driving under the influence of alcohol, as a function of a driver's age, \(x\). a. Graph the function in a [0,70,5] by [0,400,20] viewing rectangle. b. Describe the trend shown by the graph. c. Use the \([\mathrm{ZOOM}]\) and \([\mathrm{TRACE}]\) features or the maximum function feature of your graphing utility to find the age that corresponds to the greatest number of arrests. How many arrests, per 100,000 drivers, are there for this age group?
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