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Exercises Roots and quadratic equations

Example 10.37 from Elementary Algebra, 10.3 Solve Quadratic Equations Using the Quadratic Formula

Solve Quadratic Equations Using the Quadratic Formula: example 10.37

Identify the most appropriate method to use to solve each quadratic equation:

ⓐ $5 z^{2} = 17$ ⓑ $4 x^{2} - 12 x + 9 = 0$ ⓒ $8 u^{2} + 6 u = 11$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
ⓐ $5 z^{2} = 17$

Since the equation is in the $a x^{2} = k$ , the most appropriate method is to use the Square Root Property.

ⓑ $4 x^{2} - 12 x + 9 = 0$

We recognize that the left side of the equation is a perfect square trinomial, and so Factoring will be the most appropriate method.

ⓒ $8 u^{2} + 6 u = 11$

Put the equation in standard form. $8 u^{2} + 6 u - 11 = 0$

While our first thought may be to try Factoring, thinking about all the possibilities for trial and error leads us to choose the Quadratic Formula as the most appropriate method

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Identify the most appropriate method to use to solve each quadratic equation:

ⓐ $x^{2} + 6 x + 8 = 0$ ⓑ ${(n - 3)}^{2} = 16$ ⓒ $5 p^{2} - 6 p = 9$

How did it go?

PreviousSolve Quadratic Equations Using the Quadratic Formula: example 10.36 Next Solve Applications Modeled by Quadratic Equations: example 10.38

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 10.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.