roots of the equation x^2- 4x = - 7 are 2+3i and 2-3i
What are the natures of root of quadratic equation?
Case I: ![4ac > b^2](https://tex.z-dn.net/?f=4ac%20%3E%20b%5E2)
The roots of the quadratic equation
are real and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive.
Situation II: ![b^2](https://tex.z-dn.net/?f=b%5E2)
=0
The roots and of the quadratic equation
are real and equal when a, b, and c are real numbers, a 0, and the discriminant is zero.
Case III: ![b^2](https://tex.z-dn.net/?f=b%5E2)
<0
The quadratic equation
has roots when a, b, and c are real numbers, a 0, and the discriminant is negative, but these roots are not equal and are not real. We refer to the roots in this instance as fictitious.
Case IV: Perfect square and ![b^2 - 4ac > 0](https://tex.z-dn.net/?f=b%5E2%20-%204ac%20%3E%200)
The roots of the quadratic equation
are real, rational, and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.
Quadratic Formula ![x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}](https://tex.z-dn.net/?f=x%3D%7B%5Cfrac%20%7B-b%5Cpm%20%7B%5Csqrt%20%7Bb%5E%7B2%7D-4ac%7D%7D%7D%7B2a%7D%7D)
![x^2- 4x = - 7](https://tex.z-dn.net/?f=x%5E2-%204x%20%3D%20-%207)
![x^2-4x+7=0](https://tex.z-dn.net/?f=x%5E2-4x%2B7%3D0)
Here a = 1 , b = -4 , c = 7
using quadratic formula
![x={\frac {-(-4)\pm {\sqrt {(-4)^{2}-4(1)(7)}}}{2(1)}}](https://tex.z-dn.net/?f=x%3D%7B%5Cfrac%20%7B-%28-4%29%5Cpm%20%7B%5Csqrt%20%7B%28-4%29%5E%7B2%7D-4%281%29%287%29%7D%7D%7D%7B2%281%29%7D%7D)
![x={\frac {4\pm {\sqrt {-12}}}{2}}](https://tex.z-dn.net/?f=x%3D%7B%5Cfrac%20%7B4%5Cpm%20%7B%5Csqrt%20%7B-12%7D%7D%7D%7B2%7D%7D)
![x={\ {2\pm {\ 3i}}](https://tex.z-dn.net/?f=x%3D%7B%5C%20%7B2%5Cpm%20%7B%5C%203i%7D%7D)
Learn more about quadratic equation from the link below
brainly.com/question/2279540
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