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: 
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.
are real and unequal when a, b, and c are real numbers, a 0, and the discriminant is positive.
Situation II:  
 =0
 =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.
  are real and equal when a, b, and c are real numbers, a 0, and the discriminant is zero.
Case III: 
 <0
<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.
 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 
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.
  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 


Here a = 1 , b = -4 , c = 7
using quadratic formula



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