<u>Answer-</u>
<em>The values of x, which are the roots of the polynomial are </em>
![\dfrac{11+ \sqrt{69}}{2},\ \dfrac{11- \sqrt{69}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B11%2B%20%5Csqrt%7B69%7D%7D%7B2%7D%2C%5C%20%5Cdfrac%7B11-%20%5Csqrt%7B69%7D%7D%7B2%7D)
<u>Solution-</u>
The given polynomial,
![=x^2 - 11x + 13](https://tex.z-dn.net/?f=%3Dx%5E2%20-%2011x%20%2B%2013)
We know that,
![x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Here,
a = 1, b = -11, c = 13
Putting the values,
![x=\dfrac{-(-11)\pm \sqrt{(-11)^2-4\times 1\times 13}}{2\times 1}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-%28-11%29%5Cpm%20%5Csqrt%7B%28-11%29%5E2-4%5Ctimes%201%5Ctimes%2013%7D%7D%7B2%5Ctimes%201%7D)
![=\dfrac{11\pm \sqrt{121-52}}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B11%5Cpm%20%5Csqrt%7B121-52%7D%7D%7B2%7D)
![=\dfrac{11\pm \sqrt{69}}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B11%5Cpm%20%5Csqrt%7B69%7D%7D%7B2%7D)
![\therefore x=\dfrac{11+ \sqrt{69}}{2},\ \dfrac{11- \sqrt{69}}{2}](https://tex.z-dn.net/?f=%5Ctherefore%20x%3D%5Cdfrac%7B11%2B%20%5Csqrt%7B69%7D%7D%7B2%7D%2C%5C%20%5Cdfrac%7B11-%20%5Csqrt%7B69%7D%7D%7B2%7D)
Answer:
Step-by-step explanation:
1st one
Answer:
62.83
Step-by-step explanation:
Circumference=2 pi r
diameter=20
20*pi= about 62.83
so it sould be around 62.83
Answer:
The graph of both the equation is attached below, red line is the equation of
and blue line indicates the equation of
. Their y-intercepts are also indicated.
Step-by-step explanation:
Considering the equations
![y=-x-1](https://tex.z-dn.net/?f=y%3D-x-1)
and
![y = 2x + 2](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%202)
As the slope-intercept form of the equation is
, where
is the slope of the line and
is the y-intercept.
As the equation
and comparing it with ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
So,
and ![b = -1](https://tex.z-dn.net/?f=b%20%3D%20-1)
Also the equation
and comparing it with ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
So,
and
The graph of both the equation is attached below, red line is the equation of
and blue line indicates the equation of
. Their y-intercepts are also indicated.
Keywords: y-intercept, slop-intercept form, equation, graph, slope
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