Answer:
Thus, the two root of the given quadratic equation
is 5.24 and 0.76 .
Step-by-step explanation:
Consider, the given Quadratic equation, ![x^2+4=6x](https://tex.z-dn.net/?f=x%5E2%2B4%3D6x)
This can be written as , ![x^2-6x+4=0](https://tex.z-dn.net/?f=x%5E2-6x%2B4%3D0)
We have to solve using quadratic formula,
For a given quadratic equation
we can find roots using,
...........(1)
Where,
is the discriminant.
Here, a = 1 , b = -6 , c = 4
Substitute in (1) , we get,
![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\Rightarrow x=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot 1 \cdot (4)}}{2 \cdot 1}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%5Cfrac%7B-%28-6%29%5Cpm%5Csqrt%7B%28-6%29%5E2-4%5Ccdot%201%20%5Ccdot%20%284%29%7D%7D%7B2%20%5Ccdot%201%7D)
![\Rightarrow x=\frac{6\pm\sqrt{20}}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%5Cfrac%7B6%5Cpm%5Csqrt%7B20%7D%7D%7B2%7D)
![\Rightarrow x=\frac{6\pm 2\sqrt{5}}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%5Cfrac%7B6%5Cpm%202%5Csqrt%7B5%7D%7D%7B2%7D)
![\Rightarrow x={3\pm \sqrt{5}}](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D%7B3%5Cpm%20%5Csqrt%7B5%7D%7D)
and ![\Rightarrow x_2={3-\sqrt{5}}](https://tex.z-dn.net/?f=%5CRightarrow%20x_2%3D%7B3-%5Csqrt%7B5%7D%7D)
We know
(approx)
Substitute, we get,
(approx) and
(approx)
(approx) and
(approx)
Thus, the two root of the given quadratic equation
is 5.24 and 0.76 .