Question

Select the correct answer from each drop-down menu.

Consider the following equation.

o=x^2-10x-27

Complete each statement about the solutions to the equation.

The negative solution is between ? and ? .

The positive solution is between ? and ? .

Answer 1

`\displaystyle The\:negative\:solution\:is\:between\:-2 \:and\:-3.`

`\displaystyle The\:positive\:solution\:is\:between\:13\:and\:12.`

Explanation:

Since this expression is unfactorable with rational numbers, apply the Quadratic Formula:

`\displaystyle x = -b ± (√(b^2 - 4ac))/(2a) \\ \\ x = 10 ± (√([-10]^2 - 4[1][-27]))/(2[1]) \\ \\ x = 10 ± (√(100 + 108))/(2) \\ \\ x = 5 ± √(208) \\ \\ x = 5 ± 2√(13)`

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