Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
For this case we have the following polynomial:
[tex]3x^2-2x+7=0[/tex]
To solve the problem, we must complete squares.
The first step is to divide the entire expression by 3.
We have then:
[tex]\frac{3}{3}x^2-\frac{2}{3}x+\frac{7}{3}=0[/tex]
The second step is to place the constant term on the right side of the equation:
[tex] \frac{3}{3}x^2-\frac{2}{3}x=-\frac{7}{3} [/tex]
The third step is to complete the square:
[tex] \frac{3}{3}x^2-\frac{2}{3}x + (-\frac{1}{3})^2=-\frac{7}{3}+ (-\frac{1}{3})^2 [/tex]
Rewriting we have:
[tex] x^2-\frac{2}{3}x + \frac{1}{9}=-\frac{7}{3}+ \frac{1}{9} [/tex]
[tex] (x-\frac{1}{3})^2 = -\frac{20}{3} [/tex]
Answer:
By completing squares we have:
[tex] (x-\frac{1}{3})^2 = -\frac{20}{3} [/tex]
Answer:
[tex]-\dfrac{20}{9}[/tex]
Explanation:
A quadratic function is a kind of function with highest degree 2 . Standard form of the quadratic equation : tex]ax^2+bx+c=0[/tex]
Further explanation:
Consider the given quadratic equation : [tex]3x^2-2x+7=0[/tex]
First we divide both sides by 3 , we get
[tex]x^2-\dfrac{2}{3}x+\dfrac{7}{3}=0[/tex]--------(1)
Compare this equation to [tex]x^2+2ax+a^2[/tex] , we have
[tex]2a=\dfrac{-2}{3}[/tex]
[tex]\Rightarrow\ a=\dfrac{-1}{3}[/tex] [divide both sides by 2]
Now using the completing the squares method , Add and subtract [tex](\dfrac{-1}{3})^2[/tex] to the left side in (1), we get
[tex]x^2-\dfrac{2}{3}x+(\dfrac{-1}{3})^2-(\dfrac{-1}{3})^2+\dfrac{7}{3}=0[/tex]
It can be written as
[tex](x^2-2(\dfrac{1}{3})x+\dfrac{1}{3})^2)-\dfrac{1}{9}+\dfrac{7}{3}=0[/tex]
Use identity [tex]x^2-2ax+a^2=(x-a)^2[/tex], we have
[tex](x-\dfrac{1}{3})^2)+\dfrac{7(3)-1}{9}=0[/tex]
[tex](x-\dfrac{1}{3})^2)+\dfrac{20}{9}=0[/tex]
Subtract [tex]\dfrac{20}{9}[/tex] from both the sides , we get
[tex](x-\dfrac{1}{3})^2)=-\dfrac{20}{9}[/tex]
Therefore, the value of [tex](x-\dfrac{1}{3})^2)=-\dfrac{20}{9}[/tex]
Learn more :
- https://brainly.com/question/10449635 [Answered by Calculista]
- https://brainly.com/question/1596209 [Answered by AkhileshT]
Keywords :
Quadratic equation, standard form, completing squares method, Polynomial identities.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
