Algebra
Topics

# What is the discriminant of 9x^2-6x+1=0 and what does that mean?

Jul 27, 2015

For this quadratic, $\Delta = 0$, which means that the equation has one real root (a repeated root).

#### Explanation:

The general form of a quadratic equation looks like this

$a {x}^{2} + b x + c = 0$

The discriminant of a quadratic equation is defined as

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

In your case, the equation looks like this

$9 {x}^{2} - 6 x + 1 = 0$,

which means that you have

$\left\{\begin{matrix}a = 9 \\ b = - 6 \\ c = 1\end{matrix}\right.$

The discriminant will thus be equal to

$\Delta = {\left(- 6\right)}^{2} - 4 \cdot 9 \cdot 1$

$\Delta = 36 - 36 = \textcolor{g r e e n}{0}$

When the discrimiannt is equal to zero, the quadratic will only have one distinct real solution, derived from the general form

${x}_{1 , 2} = \frac{- b \pm \sqrt{\Delta}}{2 a} = \frac{- 6 \pm \sqrt{0}}{2 a} = \textcolor{b l u e}{- \frac{b}{2 a}}$

In your case, the equation has one distinct real solution equal to

${x}_{1} = {x}_{2} = - \frac{\left(- 6\right)}{2 \cdot 9} = \frac{6}{18} = \frac{1}{3}$

##### Impact of this question
1942 views around the world
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8943761587142944, "perplexity": 636.139154883939}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347411862.59/warc/CC-MAIN-20200531053947-20200531083947-00500.warc.gz"}